Glass-based articles with improved fracture resistance

ABSTRACT

Glass-based articles are provided that exhibit improved fracture resistance. The relationships between properties attributable to the glass composition and stress profile of the glass-based articles are provided that indicate improved fracture resistance.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority under 35 U.S.C. § 119 ofU.S. Provisional Application Ser. No. 62/729,735 filed on Sep. 11, 2018the content of which is relied upon and incorporated herein by referencein its entirety.

BACKGROUND Field

The present specification generally relates to glass-based articlessuitable for use as cover glass for electronic devices.

Technical Background

The mobile nature of portable devices, such as smart phones, tablets,portable media players, personal computers, and cameras, makes thesedevices particularly vulnerable to accidental dropping on hard surfaces,such as the ground. These devices typically incorporate cover glasses,which may become damaged upon impact with hard surfaces. In many ofthese devices, the cover glasses function as display covers, and mayincorporate touch functionality, such that use of the devices isnegatively impacted when the cover glasses are damaged.

There are two major failure modes of cover glass when the associatedportable device is dropped on a hard surface. One of the modes isflexure failure, which is caused by bending of the glass when the deviceis subjected to dynamic load from impact with the hard surface. Theother mode is sharp contact failure, which is caused by introduction ofdamage to the glass surface. Impact of the glass with rough hardsurfaces, such as asphalt, granite, etc., can result in sharpindentations in the glass surface. These indentations become failuresites in the glass surface from which cracks may develop and propagate.

Glass can be made more resistant to flexure failure by the ion-exchangetechnique, which involves inducing compressive stress in the glasssurface. However, the ion-exchanged glass will still be vulnerable todynamic sharp contact, owing to the high stress concentration caused bylocal indentations in the glass from the sharp contact. Additionally,ion-exchanged glass articles can exhibit an undesirable fracturecondition that results in a high number of fragments and/or energizedfragments due to stored energy in the glass.

It has been a continuous effort for glass makers and handheld devicemanufacturers to improve the resistance of handheld devices to sharpcontact failure. Solutions range from coatings on the cover glass tobezels that prevent the cover glass from impacting the hard surfacedirectly when the device drops on the hard surface. However, due to theconstraints of aesthetic and functional requirements, it is verydifficult to completely prevent the cover glass from impacting the hardsurface.

It is also desirable that portable devices be as thin as possible.Accordingly, in addition to strength, it is also desired that glasses tobe used as cover glass in portable devices be made as thin as possible.Thus, in addition to increasing the strength of the cover glass, it isalso desirable for the glass to have mechanical characteristics thatallow it to be formed by processes that are capable of making thin glassarticles, such as thin glass sheets.

Accordingly, a need exists for glasses that can be strengthened, such asby ion exchange, and that does not exhibit a high number of fragmentswhen fractured.

SUMMARY

According to aspect (1), a glass-based article is provided. Theglass-based article comprises: a first surface; a second surface; and astress profile having a first compressive region extending from a firstsurface to a first depth of compression DOC₁, a second compressiveregion extending from a second surface to a second depth of compressionDOC₂, and a tensile region extending from DOC₁ to DOC₂. The tensileregion has a tensile stress factor K_(T) greater than or equal to 1.31MPa·√(m) and less than 1.8·K_(IC), wherein K_(IC) is the fracturetoughness of a glass-based substrate having the same composition as thecenter of the glass-based article.

According to aspect (2), the glass-based article of aspect (1) isprovided, wherein K_(T) is greater than or equal to 1.41 MPa·√(m).

According to aspect (3), the glass-based article of aspect (1) or (2) isprovided, wherein K_(T) is greater than or equal to 2.0 MPa·√(m).

According to aspect (4), the glass-based article of any of aspects (1)to (3) is provided, wherein K_(T) is less than or equal to 1.781·K_(IC).

According to aspect (5), the glass-based article of any of aspects (1)to (4) is provided, wherein K_(IC) is greater than or equal to 0.67MPa·√(m).

According to aspect (6), the glass-based article of any of aspects (1)to (5) is provided, wherein K_(IC) is greater than or equal to 1.3MPa·√(m).

According to aspect (7), the glass-based article of any of aspects (1)to (6) is provided, comprising an alkali aluminosilicate.

According to aspect (8), the glass-based article of any of aspects (1)to (7) is provided, wherein DOC₁=DOC₂, as measured from the first andsecond surfaces, respectively.

According to aspect (9), the glass-based article of any of aspects (1)to (8) is provided, wherein the glass-based article is non-frangible.

According to aspect (10), a consumer electronic product is provided. Theconsumer electronic product, comprising: a housing comprising a frontsurface, a back surface and side surfaces; electrical components atleast partially within the housing, the electrical components comprisingat least a controller, a memory, and a display, the display at oradjacent the front surface of the housing; and a cover substratedisposed over the display. A portion of at least one of the housing orthe cover substrate comprises the glass-based article of any of aspects(1) to (9).

According to aspect (11), a glass-based article is provided. Theglass-based article: a surface; and a stress profile having acompressive region extending from a surface to a depth of compressionDOC, and a tensile region. The tensile region has a tensile stressfactor K_(T) greater than or equal to 1.31 MPa·√(m) and less than orequal to K_(T) ^(limit), where K_(T) ^(limit) is defined by:

$K_{T}^{limit} = {{1.716 \cdot K_{IC}}\sqrt{1 + {2.263\frac{DOC}{t}}}}$wherein K_(IC) is the fracture toughness of a glass-based substratehaving the same composition is the center of the glass-based article,and t is the thickness of the glass-based article.

According to aspect (12), the glass-based article of aspect (11) isprovided, wherein K_(T) is greater than or equal to 1.41 MPa·√(m).

According to aspect (13), the glass-based article of aspect (11) or (12)is provided, wherein K_(T) is greater than or equal to 2.0 MPa·√(m).

According to aspect (14), the glass-based article of any of aspects (11)to (13) is provided, wherein

$\frac{DOC}{t}$is greater than 0.12.

According to aspect (15), the glass-based article of any of aspects (11)to (14) is provided, wherein

$\frac{DOC}{t}$is greater than 0.18.

According to aspect (16), the glass-based article of any of aspects (11)to (15) is provided, wherein K_(IC) is greater than or equal to 0.67MPa·√(m).

According to aspect (17), the glass-based article of any of aspects (11)to (16) is provided, wherein K_(IC) is greater than or equal to 1.3MPa·√(m).

According to aspect (18), the glass-based article of any of aspects (11)to (17) is provided, comprising an alkali aluminosilicate.

According to aspect (19), the glass-based article of any of aspects (11)to (18) is provided, wherein the glass-based article is non-frangible.

According to aspect (20), a consumer electronic product is provided. Theconsumer electronic product, comprising: a housing comprising a frontsurface, a back surface and side surfaces; electrical components atleast partially within the housing, the electrical components comprisingat least a controller, a memory, and a display, the display at oradjacent the front surface of the housing; and a cover substratedisposed over the display. A portion of at least one of the housing orthe cover substrate comprises the glass-based article of any of aspects(11) to (19).

According to aspect (21), a glass-based article is provided. Theglass-based article, comprising: a first surface; a second surface; anda stress profile having a first compressive region extending from afirst surface to a first depth of compression DOC₁, a second compressiveregion extending from a second surface to a second depth of compressionDOC₂, and a tensile region extending from DOC₁ to DOC₂. The tensileregion has a tensile stress factor K_(T) greater than or equal to 1.31MPa·√(m) and less than or equal to K_(T) ^(limit), where K_(T) ^(limit)is defined by:

$K_{T}^{limit} = {{2.504 \cdot K_{IC}}\sqrt{1 - {0.531\frac{{{DOC}_{1} - {DOC}_{2}}}{t}}}}$wherein K_(IC) is the fracture toughness of a glass-based substratehaving the same composition as the center of the glass-based article, tis the thickness of the glass-based article, and the DOC₁ and the DOC₂are measured from the first surface.

According to aspect (22), the glass-based article of aspect (21) isprovided, wherein K_(T) is greater than or equal to 1.41 MPa·√(m).

According to aspect (23), the glass-based article of aspect (21) or (22)is provided, wherein K_(T) is greater than or equal to 2.0 MPa·√(m).

According to aspect (24), the glass-based article of any of aspects (21)to (23) is provided, wherein K_(T) is less than or equal to 0.95·K_(T)^(limit).

According to aspect (25), the glass-based article of any of aspects (21)to (24) is provided, wherein K_(T) is less than or equal to 0.85·K_(T)^(limit).

According to aspect (26), the glass-based article of any of aspects (21)to (25) is provided, wherein K_(IC) is greater than or equal to 0.67MPa·√(m).

According to aspect (27), the glass-based article of any of aspects (21)to (26) is provided, wherein K_(IC) is greater than or equal to 1.3MPa·√(m).

According to aspect (28), the glass-based article of any of aspects (21)to (27) is provided, comprising an alkali aluminosilicate.

According to aspect (29), the glass-based article of any of aspects (21)to (28) is provided, wherein DOC₁=t-DOC₂.

According to aspect (30), the glass-based article of any of aspects (21)to (29) is provided, wherein the glass-based article is non-frangible.

According to aspect (31), a consumer electronic product is provided. Theconsumer electronic product, comprising: a housing comprising a frontsurface, a back surface and side surfaces; electrical components atleast partially within the housing, the electrical components comprisingat least a controller, a memory, and a display, the display at oradjacent the front surface of the housing; and a cover substratedisposed over the display. A portion of at least one of the housing orthe cover substrate comprises the glass-based article of any of aspects(21) to (30).

According to aspect (32), a glass-based article is provided. Theglass-based article, comprising: a surface; and a stress profile havinga compressive region extending from a surface to a depth of compressionDOC, and a tensile region. The compressive region has acompressive-stress factor K_(CS), the tensile region has a tensilestress factor K_(T) greater than or equal to 1.31 MPa·√(m), and:

${\frac{K_{T}^{2}}{K_{1\; C}^{2}} + {\frac{1}{28.5}\frac{K_{CS}^{2}}{K_{1\; C}^{2}}}} \leq 4.45$wherein K_(IC) is the fracture toughness of a glass-based substratehaving the same composition as the center of the glass-based article.

According to aspect (33), the glass-based article of aspect (32) isprovided, wherein:

${\frac{K_{T}^{2}}{K_{1\; C}^{2}} + {\frac{1}{28.5}\frac{K_{CS}^{2}}{K_{1\; C}^{2}}}} \leq {4.1.}$

According to aspect (34), the glass-based article of aspect (32) or (33)is provided, wherein:

${\frac{K_{T}^{2}}{K_{1\; C}^{2}} + {\frac{1}{28.5}\frac{K_{CS}^{2}}{K_{1\; C}^{2}}}} \leq {3.8.}$

According to aspect (35), the glass-based article of any of aspects (32)to (34) is provided, wherein K_(T) is greater than or equal to 1.41MPa·√(m).

According to aspect (36), the glass-based article of any of aspects (32)to (35) is provided, wherein K_(T) is greater than or equal to 2.0MPa·√(m).

According to aspect (37), the glass-based article of any of aspects (32)to (36) is provided, comprising an alkali aluminosilicate.

According to aspect (38), the glass-based article of any of aspects (32)to (37) is provided, wherein the glass-based article is non-frangible.

According to aspect (39), a consumer electronic product is provided. Theconsumer electronic product, comprising: a housing comprising a frontsurface, a back surface and side surfaces; electrical components atleast partially within the housing, the electrical components comprisingat least a controller, a memory, and a display, the display at oradjacent the front surface of the housing; and a cover substratedisposed over the display. A portion of at least one of the housing orthe cover substrate comprises the glass-based article of any of aspects(32) to (38).

Additional features and advantages will be set forth in the detaileddescription which follows, and in part will be readily apparent to thoseskilled in the art from that description or recognized by practicing theembodiments described herein, including the detailed description whichfollows, the claims, as well as the appended drawings.

It is to be understood that both the foregoing general description andthe following detailed description describe various embodiments and areintended to provide an overview or framework for understanding thenature and character of the claimed subject matter. The accompanyingdrawings are included to provide a further understanding of the variousembodiments, and are incorporated into and constitute a part of thisspecification. The drawings illustrate the various embodiments describedherein, and together with the description serve to explain theprinciples and operations of the claimed subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is representation of a non-frangible sample after a frangibilitytest;

FIG. 2 is a representation of a frangible sample after a frangibilitytest;

FIG. 3 is a schematic representation of a sample utilized to determinethe fracture toughness K_(IC) and a cross-section thereof,

FIG. 4 schematically depicts a cross section of a glass-based articlehaving compressive stress layers on surfaces thereof according toembodiments disclosed and described herein;

FIG. 5 is a plot of the bifurcations per crack branch as a function oftensile stress factor K_(T) for various compositions;

FIG. 6 is a plot of frangibility limit value of K_(T) for thecompositions of FIG. 5 as a function of fracture toughness K_(IC);

FIG. 7 is a plot of the number of fragments after fracture as a functionof K_(T) for samples of composition 2 with a variety of thicknesses andion exchange treatments;

FIG. 8 is a plot of the square of the max non-frangible K_(T) as afunction of DOC/t for samples of composition 2;

FIG. 9 is a plot of the data from FIG. 8 as a function of BTZ/t;

FIG. 10 is a plot of the data from FIGS. 7 and 8 after combination withdata on the integral of the squared stress in the compressive stressregions, where K_(T) and K_(CS) are tensile and compressive stressfactors, respectively;

FIG. 11 is a plot of the data from FIGS. 7 and 8 after combination withdata on the integral of the squared stress in the compressive stressregions, where K_(Tn) and K_(CSn) are tensile and compressive stressfactors, respectively, normalized to the fracture toughness;

FIG. 12A is a plan view of an exemplary electronic device incorporatingany of the glass-based articles disclosed herein; and

FIG. 12B is a perspective view of the exemplary electronic device ofFIG. 12A.

DETAILED DESCRIPTION

Reference will now be made in detail to glass-based articles accordingto various embodiments. As utilized herein, “glass-based” indicates anarticle that includes a glass, such as glass or glass-ceramiccompositions, wherein a glass-ceramic includes one or more crystallinephases and a residual glass phase. In general, a “glass-based substrate”refers to an article prior to ion exchange, and a “glass-based article”refers to an ion exchanged article.

The glass-based articles exhibit improved drop performance while alsonot exhibiting a fracture condition that produces a large number offragments. This quality makes the glass-based articles particularlysuitable for use in electronic devices, particularly mobile electronicdevices that may be subjected to conditions causing the glass-basedarticle to fracture during use. The glass-based articles include acompressive stress layer extending from a surface of the glass-basedarticle to a depth of compression.

The effect of the particular combination of properties attributable tothe glass composition and the properties attributable to the stressprofile of the glass-based articles may be considered as a whole whenselecting glass-based articles for use in electronic devices. Stateddifferently the behavior of ion exchanged glass-based articles may beattributed to factors associated with the composition of the glass-basedsubstrate subjected to ion exchange to form the glass-based article andalso to factors attributable to the stress profile produced by the ionexchange process.

As the degree to which glass-based articles are chemically strengthened,such as by ion exchange, increases in pursuit of ever greater fractureresistance the risk that the glass-based article will exhibitundesirable fracture conditions that produce a high number of fragments,sometimes referred to as frangibility, has increased. Previously,criteria for avoiding frangibility in strengthened glasses have beenbased on limiting the maximum central tension (CT), the stored strainenergy (SSE) or the tensile-stress factor (K_(T)) of the strengthenedglass-based article. However, these limits are not universallyapplicable. Described herein are new criteria for determining thefrangibility of a glass-based article, particularly those with higherfracture toughness and/or depths of compression relative to thicknessthan previous glass-based articles. These criteria are based onrelationships between properties of the glass-based substrate utilizedto form the glass-based article, such as the fracture toughness andYoung's modulus, and properties of the stress profile, such as the depthof compression and the tensile-stress factor. Additionally, thesecriteria may be applied without destruction of the glass-based articlein some embodiments, allowing use in quality control applications.

As utilized herein, a glass-based article is considered “non-frangible”when it exhibits at least one of the following in a test area as theresult of a frangibility test: (1) four or less fragments with a largestdimension of at least 1 mm, and/or (2) the number of bifurcations isless than or equal to 1.5 bifurcations per crack branch. The fragments,bifurcations, and crack branches are counted based on any 5 cm by 5 cmsquare centered on the impact point. Thus, a glass is considerednon-frangible if it meets one or both of tests (1) and (2) for any 5 cmby 5 cm square centered on the impact point where the breakage iscreated according to the procedure described below. In a frangibilitytest, an impact probe is brought in to contact with the glass, with thedepth to which the impact probe extends into the glass increasing insuccessive contact iterations. The step-wise increase in depth of theimpact probe allows the flaw produced by the impact probe to reach thetension region while preventing the application of excessive externalforce that would prevent the accurate determination of the frangiblebehavior of the glass. The glass-based article is placed on a steelsurface such as a MVN precision vertical stage available from NewportCorporation. The impact probe is a stylus with a tungsten carbide tip(available from Fisher Scientific Industries, under the trademark TOSCO®and manufacturer identifying number #13-378, with a 60 degreeconi-spherical tip), having a weight of 40 g, and is connected to aclamp on a gear driven mechanism that moves the stylus up and down. Inone embodiment, the depth of the impact probe in the glass may increaseby about 5 μm in each iteration, with the impact probe being removedfrom contact with the glass between each iteration. The test area is any5 cm by 5 cm square centered at the impact point. FIG. 1 depicts anon-frangible test result. As shown in FIG. 1, the test area is a squarethat is centered at the impact point 135, where the length of a side ofthe square d is 5 cm. The non-frangible sample shown in FIG. 1 includesthree fragments 142, and two crack branches 140 and a single bifurcation150. Thus, the non-frangible sample shown in FIG. 1 contains less than 4fragments having a largest dimension of at least 1 mm and the number ofbifurcations is less than or equal to the number of crack branches (0.5bifurcations per crack branch). As utilized herein, a crack branchoriginates at the impact point, and a fragment is considered to bewithin the test area if any part of the fragment extends into the testarea. While coatings, adhesive layers, and the like may be used inconjunction with the strengthened glass-based articles described herein,such external restraints are not used in determining the frangibility orfrangible behavior of the glass-based articles. In some embodiments, afilm that does not impact the fracture behavior of the glass-basedarticle may be applied to the glass-based article prior to thefrangibility test to prevent the ejection of fragments from theglass-based article, increasing safety for the person performing thetest.

A frangible sample is depicted in FIG. 2. The frangible sample includes6 fragments 142 having a largest dimension of at least 1 mm. The sampledepicted in FIG. 2 includes 2 crack branches 140 and 4 bifurcations 150,producing more bifurcations than crack branches (2 bifurcations percrack branch). Thus, the sample depicted in FIG. 2 does not exhibit fouror less fragments or less than or equal to 1.5 bifurcations per crackbranch. While FIGS. 1 and 2 include two crack branches 140 originatingat the impact point 135, it is understood that more than two crackbranches may originate at the impact point, such as three or more crackbranches.

In the frangibility test described herein, the impact is delivered tothe surface of the glass article with a force that is just sufficient torelease the internally stored energy present within the strengthenedglass article. That is, the point impact force is sufficient to createat least one new crack at the surface of the strengthened glass sheetand extend the crack through the compressive stress CS region (i.e.,past the depth of compression) into the central tension region.

Accordingly, the glass-based articles described herein are“non-frangible” i.e., they do not exhibit frangible behavior asdescribed hereinabove when subjected to impact by a sharp object.

Previously, the most widely applicable empirical frangibility limit forchemically strengthened glass-based articles was based on storedtensile-strain energy in the tension region of the strengthenedglass-based article. As utilized herein, the term tensile-strain energy(TSE) represents the energy stored in the tension zone of a unit area ofa glass-based article sheet (1 square meter). The TSE limit has beenobserved to be about 18 J/m², where each of the two mutually orthogonaldimensions x and y parallel to the surface of the glass-based article isallowed a budget of about 9 J/m². The TSE per dimension (x and y) isgiven by:

${{TSE}_{x} = {\frac{1 - v}{2\; E}{\int_{{DOC}_{1}}^{{DOC}_{2}}{{\sigma_{x}^{2}(z)}d\; z}}}}\ $${TSE}_{y} = {\frac{1 - v}{2\; E}{\int_{{DOC}_{1}}^{{DOC}_{2}}{{\sigma_{y}^{2}(z)}d\; z}}}$where E is the Young's modulus, v is the Poisson's ratio, DOC₁ is thefirst depth of compression, DOC₂ is the second depth of compression, zis the position in the thickness direction, and σ_(x) and σ_(y) are thecomponents of the stress tensor in the plane parallel to the glass-basedarticle surface, in the direction of the corresponding x and y axes thatdefine the 2-dimensional space of the glass-based article. In theinterior of the area of a glass-based article sheet these two componentsof the in-plane stress are approximately equal, so they each carry aboutthe same strain energy, and the frangibility limit for the totaltensile-strain energy of 18 J/m² can be replaced by a limit of 9 J/m²for a single component of the in-plane stress, e.g., σ_(x).

In a related approach, a frangibility limit has previously been definedin terms of a quantity labeled K_(T), having the units ofstress-intensity factor, e.g., MPa√{square root over (m)}. As utilizedherein, the quantity K_(T) is the tensile-stress factor given by theequation:

$K_{T} = \sqrt{\int_{{DOC}_{1}}^{{DOC}_{2}}{{\sigma^{2}(z)}d\; z}}$where σ is represented by one of the in-plane components (as thein-plane components are presumed to be equal), and z is the position inthe thickness direction. To obtain the values of K_(T) in units ofMPa√{square root over (m)}, the stress values under the integral shouldbe in MPa, while the thickness position scale z should be in m.

U.S. Pat. No. 9,604,876 B2 discloses in Table 2 that samples with aK_(T) of 1.4 MPa√{square root over (m)} and higher produce a largenumber of fragments when fractured, while samples with K_(T) of 1.3MPa√{square root over (m)} or less do not produce excessivefragmentation. At the same time, the maximum central tension (CT) insidethe tension zone was 74 MPa and 72 MPa for the highly fragmentedexamples, and not exceeding 68 MPa for all other examples. It should benoted that in most cases typical of chemical strengthening, the CT is atthe middle of the thickness of the glass sheet. These examples areapproximately consistent with the publication by E. Bouyne and O. Gaume,“Fragmentation of thin chemically tempered glass plates”, GlassTechnology 2002, 43C, pp. 300-302, where a high degree of fragmentationis reported with increasing values of K_(T), and all samples with K_(T)of 1.4 MPa√{square root over (m)} or higher had produced a large numberof fragments (at least 5 in a 5 cm×5 cm square area).

As utilized herein, the “frangibility limit” represents the boundarybetween the conditions where a glass-based article exhibits excessivefragmentation (frangible) and where the glass-based article does notexhibit excessive fragmentation (non-frangible). The condition at thefrangibility limit may be expressed in terms of a critical(frangibility-limit) value of a parameter such as the tensile-strainenergy TSE or the tensile-stress factor K_(T) that has been shown tocorrelate with the degree of fragmentation. The total tensile-strainenergy (accounting for both x and y dimensions of strain) is related tothe tensile-strain factor K_(T) measured for a single stress component(x or y) by the equation:

${T\; S\; E} = {\frac{1 - v}{E}K_{T}^{2}}$

When the stress components along x and y differ substantially and can bemeasured, the tensile-strain energy stored in each dimension can becalculated individually as follows:

${T\; S\; E_{x}} = {\frac{1 - v}{E}K_{T,x}^{2}}$${T\; S\; E_{y}} = {\frac{1 - v}{E}K_{T,y}^{2}}$

The frangibility limit values of TSE and described herein K_(T) dependat least in part on the material properties, such as fracture toughness,of the glass-based substrate utilized to form the glass-based article,and on the parameters of the stress profile, such as the ratio of thedepth of compression to the thickness, of the glass-based article.Stated differently, the frangibility limits described herein take in toaccount the fracture toughness that was not considered in previousfrangibility determinations.

Generally, the properties described herein that refer to a glass havinga composition equivalent to the composition at the center of theglass-based article are dependent on the composition of the glass-basedsubstrate that was ion exchanged to form the glass-based article. Inpractice, the composition at the center of the glass-based article maybe measured by techniques known in the art, and the fracture toughness(K_(IC)) and Young's modulus (E) values of glass compositions producedhaving the measured composition may be measured. Additionally, thecenter of the glass-based article is not affected by or minimallyaffected by the ion exchange process, such that the composition at thecenter of the glass-based article is substantially the same or the sameas the composition of the glass-based substrate. For this reason, theK_(IC) and E values, among others, of a glass composition having thecomposition at the center of the glass-based article may be determinedby measuring these properties of the glass-based substrate before theion exchange treatment.

The properties of the glass-based articles will now be discussed. Theseproperties can be achieved by modifying the component amounts of theglass-based composition or the stress profile of the glass-basedarticle.

Compositions utilized to form the glass-based articles according toembodiments have a high fracture toughness (K_(IC)). In someembodiments, the compositions utilized to form the glass-based articlesexhibit a K_(IC) value greater than or equal to 0.67 MPa√{square rootover (m)}, such as greater than or equal to 0.68 MPa√{square root over(m)}, greater than or equal to 0.69 MPa√{square root over (m)}, greaterthan or equal to 0.70 MPa√{square root over (m)}, greater than or equalto 0.71 MPa√{square root over (m)}, greater than or equal to 0.72MPa√{square root over (m)}, greater than or equal to 0.73 MPa√{squareroot over (m)}, greater than or equal to 0.74 MPa√{square root over(m)}, greater than or equal to 0.75 MPa√{square root over (m)}, greaterthan or equal to 0.76 MPa√{square root over (m)}, greater than or equalto 0.77 MPa√{square root over (m)}, greater than or equal to 0.78MPa√{square root over (m)}, greater than or equal to 0.79 MPa m^(0.5),greater than or equal to 0.80 MPa m^(0.5), greater than or equal to 0.81MPa√{square root over (m)}, greater than or equal to 0.82 MPa√{squareroot over (m)}, greater than or equal to 0.83 MPa√{square root over(m)}, greater than or equal to 0.84 MPa√{square root over (m)}, greaterthan or equal to 0.86 MPa√{square root over (m)}, greater than or equalto 0.87 MPa√{square root over (m)}, greater than or equal to 0.88MPa√{square root over (m)}, greater than or equal to 0.89 MPa√{squareroot over (m)}, greater than or equal to 0.90 MPa√{square root over(m)}, greater than or equal to 0.91 MPa√{square root over (m)}, greaterthan or equal to 0.92 MPa√{square root over (m)}, greater than or equalto 0.93 MPa√{square root over (m)}, greater than or equal to 0.94MPa√{square root over (m)}, greater than or equal to 0.95 MPa√{squareroot over (m)}, greater than or equal to 0.96 MPa√{square root over(m)}, greater than or equal to 0.97 MPa√{square root over (m)}, greaterthan or equal to 0.98 MPa√{square root over (m)}, greater than or equalto 0.99 MPa√{square root over (m)}, greater than or equal to 1.00MPa√{square root over (m)}, greater than or equal to 1.01 MPa√{squareroot over (m)}, greater than or equal to 1.02 MPa√{square root over(m)}, greater than or equal to 1.03 MPa√{square root over (m)}, greaterthan or equal to 1.04 MPa√{square root over (m)}, greater than or equalto 1.05 MPa√{square root over (m)}, greater than or equal to 1.06MPa√{square root over (m)}, greater than or equal to 1.07 MPa√{squareroot over (m)}, greater than or equal to 1.08 MPa√{square root over(m)}, greater than or equal to 1.09 MPa√{square root over (m)}, greaterthan or equal to 1.10 MPa√{square root over (m)}, greater than or equalto 1.11 MPa√{square root over (m)}, greater than or equal to 1.12MPa√{square root over (m)}, greater than or equal to 1.13 MPa√{squareroot over (m)}, greater than or equal to 1.14 MPa√{square root over(m)}, greater than or equal to 1.15 MPa√{square root over (m)}, greaterthan or equal to 1.16 MPa√{square root over (m)}, greater than or equalto 1.17 MPa√{square root over (m)}, greater than or equal to 1.18MPa√{square root over (m)}, greater than or equal to 1.19 MPa√{squareroot over (m)}, greater than or equal to 1.20 MPa√{square root over(m)}, greater than or equal to 1.21 MPa√{square root over (m)}, greaterthan or equal to 1.22 MPa√{square root over (m)}, greater than or equalto 1.23 MPa√{square root over (m)}, greater than or equal to 1.24MPa√{square root over (m)}, greater than or equal to 1.25 MPa√{squareroot over (m)}, greater than or equal to 1.26 MPa√{square root over(m)}, greater than or equal to 1.27 MPa√{square root over (m)}, greaterthan or equal to 1.28 MPa√{square root over (m)}, greater than or equalto 1.29 MPa√{square root over (m)}, greater than or equal to 1.30MPa√{square root over (m)}, greater than or equal to 1.31 MPa√{squareroot over (m)}, greater than or equal to 1.32 MPa√{square root over(m)}, greater than or equal to 1.33 MPa√{square root over (m)}, orgreater than or equal to 1.34 MPa√{square root over (m)}. Inembodiments, the compositions utilized to form the glass-based articlesexhibit a K_(IC) value greater than or equal to 0.67 MPa√{square rootover (m)} to less than or equal to 1.34 MPa√{square root over (m)}, suchas from greater than or equal to 0.68 MPa√{square root over (m)} to lessthan or equal to 1.33 MPa√{square root over (m)}, from greater than orequal to 0.70 MPa√{square root over (m)} to less than or equal to 1.32MPa√{square root over (m)}, from greater than or equal to 0.72MPa√{square root over (m)} to less than or equal to 1.31 MPa√{squareroot over (m)}, from greater than or equal to 0.74 MPa√{square root over(m)} to less than or equal to 1.30 MPa√{square root over (m)}, fromgreater than or equal to 0.76 MPa√{square root over (m)} to less than orequal to 1.29 MPa√{square root over (m)}, from greater than or equal to0.78 MPa√{square root over (m)} to less than or equal to 1.28MPa√{square root over (m)}, from greater than or equal to 0.80MPa√{square root over (m)} to less than or equal to 1.27 MPa√{squareroot over (m)}, from greater than or equal to 0.82 MPa√{square root over(m)} to less than or equal to 1.26 MPa√{square root over (m)}, fromgreater than or equal to 0.84 MPa√{square root over (m)} to less than orequal to 1.25 MPa√{square root over (m)}, from greater than or equal to0.85 MPa√{square root over (m)} to less than or equal to 1.24MPa√{square root over (m)}, from greater than or equal to 0.86MPa√{square root over (m)} to less than or equal to 1.23 MPa√{squareroot over (m)}, from greater than or equal to 0.87 MPa√{square root over(m)} to less than or equal to 1.22 MPa√{square root over (m)}, fromgreater than or equal to 0.88 MPa√{square root over (m)} to less than orequal to 1.21 MPa√{square root over (m)}, from greater than or equal to0.89 MPa√{square root over (m)} to less than or equal to 1.20MPa√{square root over (m)}, from greater than or equal to 0.90MPa√{square root over (m)} to less than or equal to 1.19 MPa√{squareroot over (m)}, from greater than or equal to 0.91 MPa√{square root over(m)} to less than or equal to 1.18 MPa√{square root over (m)}, fromgreater than or equal to 0.92 MPa√{square root over (m)} to less than orequal to 1.17 MPa√{square root over (m)}, from greater than or equal to0.93 MPa√{square root over (m)} to less than or equal to 1.16MPa√{square root over (m)}, from greater than or equal to 0.94MPa√{square root over (m)} to less than or equal to 1.15 MPa√{squareroot over (m)}, from greater than or equal to 0.95 MPa√{square root over(m)} to less than or equal to 1.14 MPa√{square root over (m)}, fromgreater than or equal to 0.96 MPa√{square root over (m)} to less than orequal to 1.13 MPa√{square root over (m)}, from greater than or equal to0.97 MPa√{square root over (m)} to less than or equal to 1.12MPa√{square root over (m)}, from greater than or equal to 0.98MPa√{square root over (m)} to less than or equal to 1.11 MPa√{squareroot over (m)}, from greater than or equal to 0.99 MPa√{square root over(m)} to less than or equal to 1.10 MPa√{square root over (m)}, fromgreater than or equal to 1.00 MPa√{square root over (m)} to less than orequal to 1.09 MPa√{square root over (m)}, from greater than or equal to1.01 MPa√{square root over (m)} to less than or equal to 1.08MPa√{square root over (m)}, from greater than or equal to 1.02MPa√{square root over (m)} to less than or equal to 1.07 MPa√{squareroot over (m)}, from greater than or equal to 1.03 MPa√{square root over(m)} to less than or equal to 1.06 MPa√{square root over (m)}, fromgreater than or equal to 1.04 MPa√{square root over (m)} to less than orequal to 1.05 MPa√{square root over (m)}, and all ranges and sub-rangesbetween the foregoing values. In some embodiments, the compositionsutilized to form the glass-based articles exhibit a K_(IC) value greaterthan or equal to 0.90 MPa√{square root over (m)}. In some embodiments,the compositions utilized to form the glass-based articles exhibit aK_(IC) value less than or equal to 1.5 MPa√{square root over (m)}.

As utilized herein, the K_(IC) fracture toughness is measured by thedouble cantilever beam (DCB) method. The K_(IC) values were measured onglass-based substrates before being ion exchanged to form theglass-based articles. The DCB specimen geometry is shown in FIG. 3 withimportant parameters being the crack length a, applied load P,cross-sectional dimensions w and 2 h, and the thickness of thecrack-guiding groove b. The samples were cut into rectangles of width 2h=1.25 cm and a thickness ranging from, w=0.3 mm to 1 mm, with theoverall length of the sample, which is not a critical dimension, varyingfrom 5 cm to 10 cm. A hole was drilled on both ends with a diamond drillto provide a means of attaching the sample to a sample holder and to theload. A crack “guiding groove” was cut down the length of the sample onboth flat faces using a wafer dicing saw with a diamond blade, leaving a“web” of material, approximately half the total plate thickness(dimension b in FIG. 3), with a height of 180 μm corresponding to theblade thickness. The high precision dimensional tolerances of the dicingsaw allow for minimal sample-to-sample variation. The dicing saw wasalso used to cut an initial crack where a=15 mm. As a consequence ofthis final operation a very thin wedge of material was created near thecrack tip (due to the blade curvature) allowing for easier crackinitiation in the sample. The samples were mounted in a metal sampleholder with a steel wire in the bottom hole of the sample. The sampleswere also supported on the opposite end to keep the samples level underlow loading conditions. A spring in series with a load cell (FUTEK,LSB200) was hooked to the upper hole which was then extended, togradually apply load, using rope and a high precision slide. The crackwas monitored using a microscope having a 5 μm resolution attached to adigital camera and a computer. The applied stress intensity, K_(P), wascalculated using the following equation:

$K_{P} = {\left\lbrack \frac{P \cdot a}{\left( {w \cdot b} \right)^{0.5}h^{1.5}} \right\rbrack\mspace{11mu}\left\lbrack {3.47 + {2.32\;\frac{h}{a}}} \right\rbrack}$

For each sample, a crack was first initiated at the tip of the web, andthen the starter crack was carefully sub-critically grown until theratio of dimensions a/h was greater than 1.5, which is required for theabove equation to accurately calculate stress intensity. At this pointthe crack length, a, was measured and recorded using a travelingmicroscope with 5 μm resolution. A drop of toluene was then placed intothe crack groove and wicked along the entire length of groove bycapillary forces, pinning the crack from moving until the fracturetoughness is reached. The load was then increased until sample fractureoccurred, and the critical stress intensity K_(IC) calculated from thefailure load and sample dimensions, with K_(P) being equivalent toK_(IC) due to the measurement method.

The Young's modulus (E) of the glass compositions utilized to form theglass-based articles has a negative correlation with the dropperformance of the glass-based articles. In embodiments, thecompositions utilized to form the glass-based articles exhibit a Young'smodulus (E) from greater than or equal to 60 GPa to less than or equalto 120 GPa, such as from greater than or equal to 62 GPa to less than orequal to 115 GPa, from greater than or equal to 64 GPa to less than orequal to 113 GPa, from greater than or equal to 66 GPa to less than orequal to 112 GPa, from greater than or equal to 68 GPa to less than orequal to 111 GPa, from greater than or equal to 70 GPa to less than orequal to 110 GPa, from greater than or equal to 72 GPa to less than orequal to 109 GPa, from greater than or equal to 74 GPa to less than orequal to 108 GPa, from greater than or equal to 76 GPa to less than orequal to 107 GPa, from greater than or equal to 78 GPa to less than orequal to 106 GPa, from greater than or equal to 80 GPa to less than orequal to 105 GPa, from greater than or equal to 82 GPa to less than orequal to 104 GPa, from greater than or equal to 84 GPa to less than orequal to 103 GPa, from greater than or equal to 86 GPa to less than orequal to 102 GPa, from greater than or equal to 88 GPa to less than orequal to 101 GPa, from greater than or equal to 90 GPa to less than orequal to 100 GPa, from greater than or equal to 91 GPa to less than orequal to 99 GPa, from greater than or equal to 92 GPa to less than orequal to 98 GPa, from greater than or equal to 93 GPa to less than orequal to 97 GPa, from greater than or equal to 94 GPa to less than orequal to 96 GPa, or equal to 95 GPa, and all ranges and sub-rangesbetween the foregoing values. In embodiments, the compositions utilizedto form the glass-based articles exhibit a Young's modulus (E) fromgreater than or equal to 80 GPa to less than or equal to 120 GPa. Insome embodiments, the compositions utilized to form the glass-basedarticles may have a Young's modulus (E) greater than or equal to 120MPa. The Young's modulus values recited in this disclosure refer to avalue as measured by a resonant ultrasonic spectroscopy technique of thegeneral type set forth in ASTM E2001-13, titled “Standard Guide forResonant Ultrasound Spectroscopy for Defect Detection in Both Metallicand Non-metallic Parts.”

The glass-based articles may have any suitable thickness. Inembodiments, the glass-based articles may have a thickness (t) fromgreater than or equal to 0.2 mm to less than or equal to 2.0 mm, such asfrom greater than or equal to 0.3 mm to less than or equal to 1.0 mm,from greater than or equal to 0.4 mm to less than or equal to 0.9 mm,from greater than or equal to 0.5 mm to less than or equal to 0.8 mm,from greater than or equal to 0.6 mm to less than or equal to 0.7 mm,and all ranges and sub-ranges between the foregoing values.

The Poisson's ratio values recited in this disclosure refer to a valueas measured by a resonant ultrasonic spectroscopy technique of thegeneral type set forth in ASTM E2001-13, titled “Standard Guide forResonant Ultrasound Spectroscopy for Defect Detection in Both Metallicand Non-metallic Parts.”

As mentioned above, the glass-based articles are strengthened, such asby ion exchange, making a glass that is damage resistant forapplications such as, but not limited to, articles for display covers orelectronic device housings. With reference to FIG. 4, the glass-basedarticle has a first region under compressive stress (e.g., first andsecond compressive layers 120, 122 in FIG. 4) extending from the surfaceto a depth of compression (DOC) of the glass-based article and a secondregion (e.g., central region 130 in FIG. 4) under a tensile stress orcentral tension (CT) extending from the DOC into the central or interiorregion of the glass-based article. As used herein, DOC refers to thedepth at which the stress within the glass-based article changes fromcompressive to tensile. At the DOC, the stress crosses from a positive(compressive) stress to a negative (tensile) stress and thus exhibits astress value of zero.

According to the convention normally used in the art, compression orcompressive stress is expressed as a negative (<0) stress and tension ortensile stress is expressed as a positive (>0) stress. Throughout thisdescription, however, CS is expressed as a positive or absolutevalue—i.e., as recited herein, CS=|CS|. The compressive stress (CS) hasa maximum at or near the surface of the glass-based article, and the CSvaries with distance d from the surface according to a function.Referring again to FIG. 4, a first segment 120 extends from firstsurface 110 to a depth d₁ and a second segment 122 extends from secondsurface 112 to a depth d₂. Together, these segments define a compressionor CS of glass-based article 100. The compressive stress of both majorsurfaces (110, 112 in FIG. 4) is balanced by stored tension in thecentral region (130) of the glass. In some embodiments, d₁=d₂ asmeasured from the first surface 110 and the second surface 112,respectively. For the sake of convenience, where a single DOC isreferred to herein, the stress profile is presumed to be symmetricalsuch that DOC₁=DOC₂ as measured from the first surface 110 and thesecond surface 112, respectively.

The stress profiles of the glass-based articles were measureddifferently based on the composition of the glass-based substrateutilized to form the glass-based article. The method utilized for sodiumaluminosilicate glasses was different than for lithium aluminosilicateglasses.

The stress profiles of glass-based articles formed from sodiumaluminosilicate (SAS) glass-based substrates strengthened via ionexchange of potassium for sodium was measured from the refractive indexprofiles for TM and TE waves obtained by using inverse-WKB profileextraction applied to the measured effective indices of guided modes forthe TM and TE waves using a prism-coupling technique, at either 633 nmor 595 nm. The stress profile was extracted to the extent of theK-penetration by subtracting the two index profiles and dividing by thestress-optic coefficient. Then an assumption was made that in thetension zone the profile starts with a parabolic shape from the DOC to adepth d_(c) at which the profile flattens, after which a constanttension equal to the profile CT extends through the mid-thickness and tothe same depth d_(c) on the other side. The depth d_(c) was chosen basedon empirical observations to equal to 1.15·DOL_(K) for composition 2which has no K in the base glass, and 1.4·DOL_(K) for compositions 1 and4 which have a substantial amount of K in the base glass prior to ionexchange, where DOL_(K) refers to “depth of layer—potassium” or thedepth of potassium penetration as a result of an ion exchange process asdetermined for single-step ion exchanged profiles by the prism-couplingstress meter FSM-6000, manufactured by Orihara Industrial Co., Ltd.(Japan). With this assumption, the through-thickness integral of tensionin the tension zone becomes a simple function of the CT when thethickness t, the DOC, and the depth d_(c) are known, and after equatingthis integral to the integral of measured compressive stress on eitherside of the tension zone (to ensure force balance), the center tensionCT is found. Knowing the value of CT, the values of K_(T) and TSE areobtained from the assumed shape of the tension zone.

The stress profiles of glass-based articles formed from lithiumaluminosilicate (LAS) glass-based substrates where the stress profilehas a deep component produced by Na exchanging for Li, and may have ashallow component obtained by K exchanging for Li or for Na and Li, thevalues of TSE and K_(T) have been obtained by combining a measurement ofCT using a properly calibrated scattered-light polarimeter (SCALP) madeby GlassStress with a measurement of DOC using a differentscattered-light polarimeter (SLP-1000) made by Orihara instruments. Whena K-enriched high-compression layer is present on the surface, ameasurement of surface compressive stress CS, spike depth of layerDOL_(sp), and knee stress CSK at DOL_(sp) using prism-coupling stressmeasurements was also utilized.

The prism-coupling measurements utilized the refracted near-field (RNF)method. The maximum CT value provided by SCALP is utilized in the RNFmethod. In particular, the stress profile measured by RNF is forcebalanced and calibrated to the maximum CT value provided by a SCALPmeasurement. The RNF method is described in U.S. Pat. No. 8,854,623,entitled “Systems and methods for measuring a profile characteristic ofa glass sample”, which is incorporated herein by reference in itsentirety. In particular, the RNF method includes placing the glassarticle adjacent to a reference block, generating apolarization-switched light beam that is switched between orthogonalpolarizations at a rate of between 1 Hz and 50 Hz, measuring an amountof power in the polarization-switched light beam and generating apolarization-switched reference signal, wherein the measured amounts ofpower in each of the orthogonal polarizations are within 50% of eachother. The method further includes transmitting thepolarization-switched light beam through the glass sample and referenceblock for different depths into the glass sample, then relaying thetransmitted polarization-switched light beam to a signal photodetectorusing a relay optical system, with the signal photodetector generating apolarization-switched detector signal. The method also includes dividingthe detector signal by the reference signal to form a normalizeddetector signal and determining the profile characteristic of the glasssample from the normalized detector signal.

To force balance the stress profile measured by RNF the stress profileis shifted vertically until the total stress-depth area in thecompression regions equals the area in the tension region. When thestress profile is symmetric, equate the area of the compression regionclosest to the reference block to the area of the half of the tensionregion that is also closest to the reference block may be equated forbetter accuracy. After force balancing, the CT of the force balanced RNFprofile is divided by the SCALP CT to find a calibration (scaling)factor. The force balanced profile is then divided by the calibrationfactor to produce a force balanced and calibrated stress profile.

The contribution of the surface spike of K to the CT is calculated by:

${CT}_{sp} = \frac{\left( {{CS} - {CS}_{K}} \right){DOL}_{sp}}{t - {DOL}_{K}}$where t is thickness of the glass-based article. The spike refers to thesteep portion of the stress profile near the surface that is potassiumenriched and exhibits high compression. In embodiments, the DOL_(sp) maybe equivalent to the DOL_(K) for glass-based articles formed fromlithium containing glass-based substrates and ion exchanged with apotassium containing salt bath. The contribution of the deep componentof the stress profile produced by the Na-for-Li ion exchange iscalculated by:CT _(deep) =CT−CT _(sp)

The Na diffusion depth for the examples of interest using LAS glasseswas comparable to the half of the glass-sheet thickness, and the shapeof the stress profile in the tension zone could be adequatelyapproximated as the absolute value of a power-law shape with powercoefficient p falling in the range 1.5-3 (where p=2 would correspond toparabolic shape). With that assumption, the exact solution for the ratioDOC/t given p, CT_(deep), and the total CT measured by SCALP is:

$\frac{DOC}{t} = {0.5\left\{ {1 - \left\lbrack \frac{CT}{\left( {1 + p} \right)\;{CT}_{deep}} \right\rbrack^{\frac{1}{p}}} \right\}}$

After measuring CT and DOC as described above, measuring the thicknesswith a micrometer, and calculated CT_(deep) the power coefficient p wasvaried until the measured DOC/t value agreed with the ratio calculatedbased on the above formula. This fixed p value, along with the CT andthe DOC, allows the tension region to be fully determined.

By assigning a value z0 to the distance from the mid-thickness of theglass-based article to the point where the point where compressionbecomes tension such that:z ₀=0.5t−DOC

The tensile-stress factor (K_(T)) and the TSE are then calculated as afunction of the power coefficient p by:

${K_{T}(p)} = {2{pCT}\;\sqrt{\frac{z_{0}}{{2\; p^{2}} + {3p} + 1}}}$${{TSE}(p)} = {\frac{1 - v}{E}\frac{4p^{2}}{{2p^{2}} + {3p} + 1}z_{0}{CT}^{2}}$

To reduce the error caused by laser-speckle and other noise sources, theCT and DOC values for each sample were averaged over at least 20measurements, each obtained from a separate scan obtained with aslightly shifted sample position on the instrument. The identificationof the location of sample surface for SLP-1000 was calibrated bymeasuring samples of SAS-glass for which DOC had been accuratelydetermined by the IWKB-based stress-profile extraction method.

Surface stress measurements rely upon the accurate measurement of thestress optical coefficient (SOC), which is related to the birefringenceof the glass. SOC in turn is measured according to Procedure C (GlassDisc Method) described in ASTM standard C770-16, entitled “Standard TestMethod for Measurement of Glass Stress-Optical Coefficient,” thecontents of which are incorporated herein by reference in theirentirety.

In some embodiments, the frangibility limit for glass-based articled interms of the tensile-stress factor K_(T) and the tensile-strain energyTSE is not a constant, but depends on the fracture toughness K_(IC) ofthe glass. FIG. 5 shows the average number of bifurcations per crackbranch as a function of the tensile-stress factor K_(T) for 3 differentSAS glass compositions having different fracture toughness. The numberof crack branches was usually 2 or 3, each originating at afracture-origin location in the center of a 5 cm×5 cm square glass-basedarticle. For the experiments in FIG. 5, the glass-based articles were0.8 mm thick. The compositions in FIG. 5 are detailed in Table 1 below.The frangibility limit for practical purposes is defined as the criticalvalue of K_(T) or TSE above which the glass-based article is frangible.For the compositions presented in FIG. 5, the critical value of 1.5bifurcations per branch occurred at a K_(T) value of 1.18, 1.215, and1.29, for Compositions 1, 2, and 3, respectively.

TABLE 1 Composition 1 2 3 4 5 6 7 8 9 SiO₂ 58.54 57.43 66.37 63.60 70.9463.31 58.35 70.72 63.70 B₂O₃ 0.60 1.86 6.74 6.07 0.39 Al₂O₃ 15.30 16.1010.29 15.67 12.83 15.20 17.81 4.28 16.18 Na₂O 16.51 17.05 13.80 10.812.36 4.30 1.73 8.10 K₂O 2.28 2.400 0.20 0.53 Li₂O 6.24 8.22 6.82 10.7422.09 8.04 MgO 1.07 2.81 5.74 2.87 1.00 4.43 0.33 ZnO 1.16 0.83 TiO₂0.004 0.003 0.003 0.010 CaO 0.59 1.55 0.57 Fe₂O₃ 0.022 <0.02 0.020 ZrO₂1.97 SnO₂ 0.10 0.07 0.21 0.04 0.06 0.05 0.08 0.08 0.05 SrO 1.02 P₂O₅6.54 6.54 2.48 0.85 2.64 K_(IC) 0.660 0.676 0.732 0.751 0.841 0.8710.948 1.335 0.795 (MPa√m) Poisson 0.205 0.215 0.211 0.210 0.200 0.2300.236 0.190 0.210 Ratio Young's 63.9 66.0 72.9 76.3 80.0 76.7 83.0 101.077.3 Modulus (GPa)

Composition 8 is a transparent glass ceramic. This composition wasformed by ceramming a precursor glass.

As shown in Tables 2 and 3 below, the examples in FIG. 5 were producedusing a single step ion exchange, with a bath primarily composed of KNO₃and a small amount of NaNO₃. The time period of the ion exchange wasvaried in the range described in Table 2 to produce samples withdifferent tensile stress factors and DOC/t. The resulting compressivestress was about 800 MPa for composition 2, and between 750 MPa and 800MPa for compositions 1 and 3. The DOC was in the range of 43 to 60 μm.The steep region of the curves shown in FIG. 5 began at a DOC aboveabout 53 μm for compositions 1 and 3, and about 47 μm for composition 2.The ratio DOC/t at the onset of the steep region of the curves in FIG. 5fell between 0.058 and 0.070 for all of the compositions.

TABLE 2 Step 1 Step 2 IOX Thickness NaNO₃ KNO₃ LiNO₃ Temperature TimeNaNO₃ KNO₃ Temperature Time Condition (mm) (wt %) (wt %) (wt %) (° C.)(hours) (wt %) (wt %) (° C.) (hours) 1 0.8 ≤1 99 0 390 2 to 4 2 0.8 1.598.5 0 420 2.7 to 3.7 3 0.8 ≤1 99 0 390 6.5 to 24  4 0.8 85 15 0 3803.75 9 91 380 0.6 5 0.9 85 15 0 380 4.5 9 91 380 0.6 6 1 85 15 0 380 5.59 91 380 0.6 7 0.8 9.5 91.5 0 430 4.25 8 0.8 100 0 0 430 7 9 0.9 100 0 0400 16 10 0.8 7 93 0 430 12 11 0.8 7 93 0 430 12 12 0.8 70 30 0.4 470 1270 30 470 1.5 13 0.8 100 0 0 470 15 14 0.8 75 25 0.6 390 3.75

IOX conditions 10 and 11 utilized the same salt concentration and sameion exchange time. However, condition 10 employed dense packing (≥0.01m² of glass per kg of salt) of the glass samples while condition 11employed less dense packing (<0.005 m² of glass per kg of salt).

TABLE 3 IOX K_(T) K_(T) ² TSE DOL_(spike) CS_(max) − CS_(K) DOCComposition Condition (MPa√m) (mPa²m) (J/m²) Frangible (μm) (MPa) (μm) 11 1.18 1.392 17.3 L 2 2 1.215 1.476 17.6 L 3 3 1.29 1.664 18 L 4 4 1.1641.354 14 N 9 700 155 4 5 1.255 1.574 16.3 N 10 700 172 4 6 1.387 1.92519.9 L/Y 10 700 187 5 7 1.486 2.207 22.1 L/Y 8 540 166 6 8 1.57 2.46524.8 N 5 1 171 6 9 1.757 3.085 31 Y 5 10 190 7 10 1.413 1.997 18.4 N 9570 180 7 11 1.569 2.461 22.7 Y 9 570 180 8 12 2.152 4.632 37.1 N 3 100155 8 13 2.598 6.75 54.1 Y 3 100 159 9 14 1.516 2.298 23.5 L 11 200 150IOX CT CT_(spike) CT_(deep) K_(T estimated) K_(CS estimated) CompositionCondition (MPa) (MPa) (MPa) p_(estimated) (MPa√m) (MPa√m) 4 4 72 8 64 21.164 4 5 72 7.9 64.1 2.1 1.255 4 6 73 7.1 65.9 2.4 1.397 5 7 97 5.591.5 1.8 1.486 2.34 6 8 101 0 101 1.95 1.57 1.966 6 9 105.5 0.1 105.4 21.757 2.22 7 10 107 6.5 100.5 1.25 1.413 2.194 7 11 117 6.5 110.5 1.31.569 2.34 8 12 125 0.4 124.6 2.6 2.152 3 8 13 155 0.4 154.6 2.4 2.5983.51 9 14 86.5 2.8 83.7 2.7 1.516 IOX K_(T) ² + (K_(CS) ²/28.5)Composition Condition K_(T)/K_(IC) (MPa²m) 5 7 1.77 3.54 6 8 1.87 3.55 69 2.09 4.45 7 10 1.68 2.59 7 11 1.87 3.16 8 12 2.56 3.29 8 13 3.09 4.73

Where “L” indicates the sample is at the frangibility limit, “N”indicates the sample is non-frangible, “Y” indicates the sample isfrangible, and “L/Y” indicates the sample was at the limit or sometimesslightly frangible.

The frangibility limit value of K_(T) for compositions 1, 2, and 3 ofFIG. 5 is shown as a function of the fracture toughness K_(IC) isdepicted in FIG. 6. A linear fit trendline through the origin provides asatisfactory fit for the experimental results in FIG. 6 when accountingfor experimental standard deviations in the measurement of K_(IC). Thislinear fit demonstrates that the frangibility limit in terms of K_(T) isproportional to the fracture toughness K_(IC), with a coefficient ofproportionality of 1.78 when DOC/t is about 0.06, as is the case for theexamples in FIG. 5. For this reason, a strengthened glass-based articleis provided in some embodiments having a tensile-stress factor K_(T)exceeding 1.3 MPa√{square root over (m)} but not exceeding the value1.78·K_(IC). Such a glass-based article has greater fracture resistancethan a glass-based article with a K_(T) below 1.3 MPa√{square root over(m)}, while remaining non-frangible. In some embodiments, thetensile-stress factor K_(T) exceeds 1.4 MPa√{square root over (m)} anddoes not exceed 1.78·K_(IC).

In some embodiments, the glass-based article is characterized by atensile-strain factor K_(T) that exceeds 1.4 MPa√{square root over (m)}and tensile-strain energy does not exceed a frangibility limit in termsof TSE given by:

${TSE}^{limit} = {\frac{1 - v}{E}{3.17 \cdot K_{IC}^{2}}}$

By way of illustration, the frangibility limit in terms of TSE may begiven by:

${{TSE}^{limit}\left\lbrack \frac{J}{m^{2}} \right\rbrack} = {37.5 \cdot K_{IC}^{2}}$when the values for the Poisson's ratio and Young's modulus ofcomposition 2 are substituted into the equation.

In embodiments, the frangibility limit of glass-based articles in termsof tensile-stress factor K_(T) or the tensile-strain energy TSE dependson the ratio DOC/t, or, alternatively, on the ratio BTZ/t, e.g., breadthof the tension zone divided by the sheet thickness. BTZ mayalternatively be indicated as DOC₂−DOC₁. FIG. 7 shows experimental datausing 6 different thicknesses of 5 cm×5 cm square sheets of glasscomposition 2, chemically strengthened by long ion exchange in a bathhaving approximately 35% or 37% NaNO₃ and 65% or 63% KNO₃ by weight, at450° C. for extended periods of time between about 13 hours and 24.5hours. The horizontal axis of FIG. 7 shows the tensile-stress factorK_(T) obtained from extraction of the stress profiles by theIWKB-method, while the vertical axis shows the logarithm with base 2 ofthe number of fragments for each fractured sample. A sample broken into5 or more fragments will have logarithm higher than 2, and wasconsidered frangible. The data for all thicknesses generally follow thesame trend, except for a few outliers. These outliers are likely due tofalse positives, e.g., when the tip of the fracturing tool was dull orthe sample had slight warp, each of which can promote the introductionof externally provided energy (potential or kinetic) by the fracturingtool to the sample. The data shown in FIG. 7 indicates that the criticalvalue of the factor K_(T) (and, correspondingly, of the TSE) does notdepend substantially on the thickness. Furthermore, the critical valueof K_(T) for the strengthening conditions represented in FIG. 7 issignificantly higher than that for the same composition 2 shown in FIG.5. One substantial difference between the samples represented in FIG. 7and the samples represented in FIG. 5 is the value of the ratio DOC/t.The samples in FIG. 5 were obtained by a relatively shallow ion exchangein mainly KNO₃ resulting in a stress profile with high surface CS around800 MPa and a moderate DOC, such that the ratio DOC/t was about 0.058for the parts of composition 2 that were at or near the frangibilitylimit. On the other hand, the samples represented in FIG. 7 werestrengthened by a significantly deeper ion exchange with lower surfaceCS in the range 240-320 MPa, and a substantially higher DOC/t ratio,between about 0.13 and 0.21, with higher ratios obtained for the smallerthicknesses and vice-versa.

For each represented thickness in FIG. 7, the tension strain energy TSEand factor K_(T) are increased by increasing the ion exchange time andthe DOC/t ratio. In the reported range of K_(T), the ratio DOC/t variedin a relatively narrow range for each thickness, 0.193-0.206 for t=0.4mm, 0.161-0.179 for t=0.5 mm, 0.164-0.177 for t=0.55 mm, 0.143-0.161 fort=0.6 mm, 0.138-0.167 for t=0.7 mm, and 0.134-0.145 for t=0.8 mm.Non-frangible samples were observed at the following highest levels ofK_(T)−1.379 MPa√{square root over (m)} for t=0.4 mm, 1.37 MPa√{squareroot over (m)} for t=0.5 mm, 1.375 MPa√{square root over (m)} for t=0.55mm, 1.36 MPa√{square root over (m)} for t=0.6 mm, 1.37 MPa√{square rootover (m)} for t=0.7 mm, and 1.344 MPa√{square root over (m)} for t=0.8mm. Frangible samples were produced for each thickness at the followinglowest levels of K_(T)−1.313 MPa√{square root over (m)} for t=0.4 mm,1.24 MPa√{square root over (m)} for t=0.5 mm, 1.368 MPa√{square rootover (m)} for t=0.55 mm, 1.376 MPa√{square root over (m)} for t=0.6 mm,1.334 MPa√{square root over (m)} for t=0.7 mm, and 1.296 MPa√{squareroot over (m)} for t=0.8 mm. If data points that stand above the generaltrend are assigned as false positives and ignored, the lowest levels ofK_(T) for frangible parts with 8 or more fragments are: 1.366MPa√{square root over (m)} for t=0.4 mm, 1.355 MPa√{square root over(m)} for t=0.5 mm, 1.368 MPa√{square root over (m)} for t=0.55 mm, 1.376MPa√{square root over (m)} for t=0.6 mm, 1.357 MPa√{square root over(m)} for t=0.7 mm, and 1.343 MPa√{square root over (m)} for t=0.8 mm.

The K_(T) values of FIGS. 5 and 7 have been squared and combined withadditional data for the same glass composition 2 obtained for thethickness of 0.4 mm and plotted in FIG. 8. The additional data includesa frangibility-limit estimate obtained for a very large ratio of DOC/tby heat treatment of frangible samples having a large ratio DOC/t above0.2 until frangible behavior is no longer observed. Such samples wereprepared by ion exchange in a bath having 35% NaNO₃ and 65% KNO₃ at 450°C. for between 14.4 and 16.5 hours, or in a bath having 17% NaNO₃ and83% KNO₃, at 430° C. for 11.5 hours followed by 450° C. for 1.25 hours.The latter samples were highly frangible, but approached thefrangibility limit after a heat treatment at 400° C. for 12 hours. TheDOC increased to about 0.23t after the heat treatment. The samplesexchanged in the bath having the higher Na content required shorter heattreatment to return to a non-frangible state from the post-ion exchangefrangible condition, as they had a lower K_(T) value after ion exchange.The data in FIG. 8 for K_(T) ² vs. DOC/t fits well to an empiricallinear model which allowed the development of a precise empiricaldependence of the frangibility-limit values for K_(T) (and TSE) on theratio DOC/t. In particular, for composition 2 the model gives:

${K_{T}^{2}{limit}} = {1.3447 + {3.0443\;\frac{DOC}{t}}}$ and:${K_{T}{limit}} = {1.16\sqrt{1 + {2.263\frac{DOC}{t}}}}$

Based on these relationships, and taking into account that the fracturetoughness K_(IC) of composition 2 is 0.767 MPa√{square root over (m)},the following empirical general relationship between thefrangibility-limit for K_(T), the fracture toughness K_(IC), and theratio DOC/t is produced:

${K_{T}{limit}} = {{1.716 \cdot K_{IC}}\sqrt{1 + {2.263\;\frac{DOC}{t}}}}$

In some embodiments, this empirical general relationship for thefrangibility-limit K_(T) may be modified by a confidence factor (CF) asfollows:

${K_{T}{limit}} = {C\;{F \cdot 1.716 \cdot K_{IC}}\sqrt{1 + {2.263\frac{DOC}{t}}}}$where the confidence factor (CF) may be given a value lower than 1, suchas in the range of 0.9 to 0.95 when avoiding fragmented failure is ofvery high importance and the limited precision of instruments allows thedetermination of K_(T) with a precision of only a few percent. Aconfidence factor (CF) with a value closer to 1, such as in the range of0.95 to 1, would be appropriate when high-precision measurements ofcritical parameters of the stress profile allow the value of K_(T) to beobtained with precision on the order of 1% or less.

Based on the relationship between TSE and K_(T), the following limitscan be equivalently applied to the TSE:

${TSE}^{limit} = {\frac{1 - v}{E}2.94\left( {{CF} \cdot K_{IC}} \right)^{2}\left( {1 + {2.263\frac{DOC}{t}}} \right)}$

For composition 2, the Poisson's ratio and the Young's modulus havevalues of 0.22 and 66 GPa, respectively. These values can be used togenerate a general TSE limit given by the following:

${{TSE}^{limit}\left( \frac{J}{m^{2}} \right)} = {34.8\;\left( {{CF} \cdot K_{IC}} \right)^{2}\left( {1 + {2.263\frac{DOC}{t}}} \right)}$

FIG. 9 shows the data of FIG. 8, as a function of BTZ/t in place ofDOC/t. A linear fit of the frangibility limit value of K_(T) ² as afunction of BTZ/t for the composition 2 data was found, given by:

${K_{T}^{2}{limit}} = {2.8664 - {1.5217\;\frac{BTZ}{t}}}$ and:${K_{T}{limit}} = {1.693\;\sqrt{1 - {0.531\;\frac{BTZ}{t}}}}$

The use of BTZ allows this relationship to be applied to glass-basedarticles with asymmetrical stress profiles, such as stress profileswhere DOC₁ is not equal to DOC₂ when measured from the first and secondsurfaces, respectively. When expressed in terms of the fracturetoughness the relationship is:

${K_{T}{limit}} = {{{{CF} \cdot 2.504 \cdot K_{IC}}\sqrt{1 = {0.531\;\frac{BTZ}{t}}}} \approx {{{CF} \cdot 2.5 \cdot K_{IC}}\sqrt{1 - {0.531\;\frac{BTZ}{t}}}}}$

The confidence factor (CF) may range from 0.85 to 1, and may be appliedin the same way described above.

An associated TSE limit is given by:

${TSE}^{limit} = {\frac{1 - v}{E}6.27\;\left( {{CF} \cdot K_{IC}} \right)^{2}\left( {1 - {0.531\;\frac{BTZ}{t}}} \right)}$

In addition, the compressive stress factor K_(CS) is equal to the squareroot of the integrated compressive stress over the compressive-stressregions on either side of the tensile-stress region, for a singlecomponent of the stress, x or y, as follows:

$K_{{CS},x} = \sqrt{\int_{{CS}_{x\; > 0}}{{\sigma_{x}^{2}(z)}{dz}}}$$K_{{CS},y} = \sqrt{\int_{{CS}_{y} > 0}{{\sigma_{y}^{2}(z)}{dz}}}$

Or generally, for either component:

$K_{CS} = \sqrt{{\int_{{CS} > 0}{{\sigma^{2}(z)}d\; z}}\ }$

In the case of a stress profile having two compressive regions extendingon either side of a central tension region, from the first surface atz=0 to the first depth of compression DOC₁, and respectively on thesecond side from the second surface z=t to DOC₂, the compressive-stressfactor takes the form:

$K_{CS} = \sqrt{{\int_{z = 0}^{{DOC}_{1}}{{\sigma^{2}(z)}{dz}}} + {\int_{t - {DOC}_{2}}^{t}{{\sigma^{2}(z)}{dz}}}}$

For symmetric stress profiles, where DOC₁=DOC₂ when measured from thefirst and second surfaces, respectively, and with a symmetric stressdistribution, the compressive stress factor is given by:

$K_{CS} = \sqrt{2{\int_{z = 0}^{DOC}{{\sigma^{2}(z)}{dz}}}}$

A compressive stress energy value of the glass-based articles may bedescribed by:

${C\; S\; E} = {\frac{1 - v}{2E}\left( {K_{{CS},x}^{2} + K_{{CS},y}^{2}} \right)}$which may be simplified when K_(CS,x)=K_(CS,y)=K_(CS) to:

${CSE} = {\frac{1 - v}{2\; E}K_{CS}^{2}}$

The apparent increase in frangibility limit in terms of K_(T) wascorrelated not only with the ratio DOC/t, but also with the relativemagnitude of TSE and CSE. In particular, with an increase of the ratioDOC/t the TSE comprised a larger fraction of the total strain energy(TSE+CSE) stored in the glass-based article as the result of chemicalstrengthening. Tables 4 and 5 include a summary of the data for samplesproduced with composition 2 and various thicknesses and stress profiles.

TABLE 4 IOX Conditions Bath Stress Average Thickness Content TemperatureTime CS DOL_(K) DOC CT Integral Tension I/t Sample (mm) (wt %) (° C.)(hours) (MPa) (μm) (μm) (MPa) (MPa · μm) (MPa) DOC/t BTZ/t (MPa) A 0.437% NaNO₃ 450 16 239 160 82.6 116.2 19520 82.8 0.2 0.6 48.7 63% KNO₃ B0.5 35% NaNO₃ 450 14.5 294 144 85.5 96.2 23675.3 72 0.17 0.66 47.4 65%KNO₃ C 0.55 35% NaNO₃ 450 13.5 297 148 90.7 80.2 25298.8 68.6 0.1660.668 46 65% KNO₃ D 0.6 35% NaNO₃ 450 15.75 304.5 147 93.4 73.1 2641864.1 0.156 0.688 44.1 65% KNO₃ E 0.7 37% NaNO₃ 450 20 278.5 175 108.768.85 28990 59.7 0.155 0.69 41.2 63% KNO₃ F 0.8 37% NaNO₃ 450 23 298 173113.2 54.3 31376 54.3 0.141 0.718 39 63% KNO₃ G 0.8 1.5% NaNO₃ 390 3 81356 48 46.3 31944 45.5 0.059 0.882 40 98.5% KNO₃ H 0.4 17% NNO₃ 430 11.5160 172 91 119 19500 89.9 0.23 0.54 48.9 83% KNO₃ I 0.4 100% KNO₃ 3901.3 930 36 29.2 67 22300 65.3 0.074 0.852 55.8

TABLE 5 A B C D E F G H I K_(T) 1.379 1.37 1.375 1.35 1.37 1.344 1.2151.418 1.244 (MPa√m) TSE 22.5 22.2 22.3 21.5 22.2 21.3 17.4 23.8 18.3(J/m²) K_(T) ² 1.903 1.878 1.892 1.823 1.877 1.806 1.476 2.01 1.548(MPa²m) K_(CS) ² 2.952 4.283 4.635 4.924 5.056 5.737 16.8 2.51 12.97(MPa²m) K_(Tn) ² 4.163 4.109 4.139 3.988 4.107 3.953 3.23 4.398 3.388(MPa²m) K_(CSn) ² 6.46 9.372 10.142 10.775 11.064 12.554 36.763 5.49328.382 (MPa²m) K_(T) ² + (K_(CS) ²/28.5) 2.006 2.028 2.054 1.995 2.0542.008 2.066 2.098 2.003 (MPa²m) K_(Tn) ² + (K_(CSn) ²/28.5) 4.39 4.4384.495 4.366 4.495 4.393 4.52 4.591 4.384 (MPa²m)

TSE is proportional to K_(T) ², while CSE is proportional to K_(CS) ².For the experiments with composition 2 it was determined that at thefrangibility limit condition a specific sum of the squared factors K_(T)and K_(CS) normalized to the fracture toughness is substantiallyunchanged regardless of the ratio DOC/t. FIG. 10 shows that for glasscomposition 2 the sum of K_(T) ² and K_(CS) ²/28.5 is constant at thefrangibility limit for the tested range of the ratio DOC/t:

${K_{T}^{2} + \frac{K_{CS}^{2}}{28.5}} = {2.03 \pm {0.04\mspace{14mu}{MPa}^{2}\mspace{14mu} m}}$

This includes non-frangible examples having K_(T) as low as 1.215MPa√{square root over (m)}, and as high as 1.418 MPa√{square root over(m)}, and additional examples at 1.244 MPa√{square root over (m)}, 1.344MPa√{square root over (m)}, 1.35 MPa√{square root over (m)}, 1.37MPa√{square root over (m)}, 1.375 MPa√{square root over (m)}, and 1.379MPa√{square root over (m)}. Hence, in embodiments, a glass articlehaving K_(T) greater than or equal to 1.2 MPa√{square root over (m)},also satisfies the condition

${K_{T}^{2} + \frac{K_{CS}^{2}}{28.5}} = {2.03\mspace{14mu}{MPa}^{2}\mspace{14mu} m}$

In embodiments, the glass-based article has a K_(T) greater than orequal to 1.24 MPa√{square root over (m)}, 1.3 MPa√{square root over(m)}, 1.34 MPa√{square root over (m)}, 1.36 MPa√{square root over (m)},1.37 MPa√{square root over (m)}, 1.4 MPa√{square root over (m)}, or 1.41MPa√{square root over (m)}. Furthermore, in some embodiments K_(T) doesnot exceed 2.2K_(IC), 2.1K_(IC), 2.0K_(IC), 1.9K_(IC), 1.8K_(IC), or1.78K_(IC), where K_(IC) is the fracture toughness of the glass, or thelocal glass composition in the location having the highest tension(usually the mid-plane of the glass sheet).

Taking into account that the fracture toughness of composition 2 is0.676 MPa√{square root over (m)}, the data of FIG. 10 are presented inFIG. 11 where the weighted contributions of K_(T) ² and K_(CS) ² havebeen normalized to the square of fracture toughness. Then to avoidfrangibility:

${K_{T}^{2} + \frac{K_{CS}^{2}}{28.5}} \leq {4.45\; K_{IC}^{2}}$ or:${\frac{K_{T}^{2}}{K_{IC}^{2}} + {\frac{1}{28.5}\frac{K_{CS}^{2}}{K_{IC}^{2}}}} \leq 4.45$

In terms of the normalized values where K_(Tn)=K_(T)/K_(IC) andK_(CSn)=K_(CS)/K_(IC) presented in FIG. 11, the condition may be furthersimplified to:

${K_{Tn}^{2} + \frac{K_{CSn}^{2}}{28.5}} \leq 4.45$

In embodiments, a glass-based article having K_(T) greater than or equalto 1.31 MPa√{square root over (m)}, also satisfies the condition:

${K_{T}^{2} + \frac{K_{CS}^{2}}{28.5}} \leq {4.45\; K_{IC}^{2}}$

More conservative criteria may also be employed, such as:

${K_{T}^{2} + \frac{K_{CS}^{2}}{28.5}} \leq {4.1\; K_{IC}^{2}}$ or:${K_{T}^{2} + \frac{K_{CS}^{2}}{28.5}} \leq {3.8\; K_{IC}^{2}}$

In embodiments, K_(T) is greater than or equal to 1.2 MPa√{square rootover (m)}, such as greater than or equal to 1.24 MPa√{square root over(m)}, greater than or equal to 1.3 MPa√{square root over (m)}, greaterthan or equal to 1.31 MPa√{square root over (m)}, greater than or equalto 1.34 MPa√{square root over (m)}, greater than or equal to 1.36MPa√{square root over (m)}, greater than or equal to 1.37 MPa√{squareroot over (m)}, greater than or equal to 1.4 MPa√{square root over (m)},greater than or equal to 1.41 MPa√{square root over (m)}, greater thanor equal to 1.43 MPa√{square root over (m)}, greater than or equal to1.44 MPa√{square root over (m)}, greater than or equal to 1.45MPa√{square root over (m)}, greater than or equal to 1.46 MPa√{squareroot over (m)}, greater than or equal to 1.47 MPa√{square root over(m)}, greater than or equal to 1.48 MPa√{square root over (m)}, greaterthan or equal to 1.49 MPa√{square root over (m)}, greater than or equalto 1.50 MPa√{square root over (m)}, greater than or equal to 1.51MPa√{square root over (m)}, greater than or equal to 1.52 MPa√{squareroot over (m)}, greater than or equal to 1.53 MPa√{square root over(m)}, greater than or equal to 1.54 MPa√{square root over (m)}, greaterthan or equal to 1.55 MPa√{square root over (m)}, greater than or equalto 1.56 MPa√{square root over (m)}, greater than or equal to 1.57MPa√{square root over (m)}, greater than or equal to 1.58 MPa√{squareroot over (m)}, greater than or equal to 1.59 MPa√{square root over(m)}, greater than or equal to 1.60 MPa√{square root over (m)}, greaterthan or equal to 1.7 MPa√{square root over (m)}, greater than or equalto 1.8 MPa√{square root over (m)}, greater than or equal to 1.9MPa√{square root over (m)}, or greater than or equal to 2 MPa√{squareroot over (m)}. In some embodiments K_(T) does not exceed 2.2K_(IC),such as being less than or equal to 2.1K_(IC), less than or equal to2.0K_(IC), less than or equal to 1.9K_(IC), less than or equal to1.8K_(IC), less than or equal to 1.78K_(IC), less than or equal to1.75K_(IC), less than or equal to 1.7K_(IC), less than or equal to1.65K_(IC), or less.

In some embodiments, the CS of the glass-based article is from greaterthan or equal to 300 MPa to less than or equal to 1300 MPa, such as fromgreater than or equal to 325 MPa to less than or equal to 1250 MPa, fromgreater than or equal to 350 MPa to less than or equal to 1200 MPa, fromgreater than or equal to 375 MPa to less than or equal to 1150 MPa, fromgreater than or equal to 400 MPa to less than or equal to 1100 MPa, fromgreater than or equal to 425 MPa to less than or equal to 1050 MPa, fromgreater than or equal to 450 MPa to less than or equal to 1000 MPa, fromgreater than or equal to 475 MPa to less than or equal to 975 MPa, fromgreater than or equal to 500 MPa to less than or equal to 950 MPa, fromgreater than or equal to 525 MPa to less than or equal to 925 MPa, fromgreater than or equal to 550 MPa to less than or equal to 900 MPa, fromgreater than or equal to 575 MPa to less than or equal to 875 MPa, fromgreater than or equal to 600 MPa to less than or equal to 850 MPa, fromgreater than or equal to 625 MPa to less than or equal to 825 MPa, fromgreater than or equal to 650 MPa to less than or equal to 800 MPa, fromgreater than or equal to 675 MPa to less than or equal to 775 MPa, orfrom greater than or equal to 700 MPa to less than or equal to 750 MPa,and all ranges and sub-ranges between the foregoing values. In someembodiments, the CS of the glass-based article is greater than or equalto 100 MPa.

The DOL_(K) is typically less than the DOC for the articles describedherein. The DOL_(K) of each of first and second compressive layers 120,122 is from greater than or equal to 5 μm to less than or equal to 30μm, such as from greater than or equal to 6 μm to less than or equal to25 μm, from greater than or equal to 7 μm to less than or equal to 20μm, from greater than or equal to 8 μm to less than or equal to 15 μm,or from greater than or equal to 9 μm to less than or equal to 10 μm,and all ranges and sub-ranges between the foregoing values. In otherembodiments, the DOL_(K) of each of the first and second compressivelayers 120, 122 is from greater than or equal to 6 μm to less than orequal to 30 μm, such as from greater than or equal to 10 μm to less thanor equal to 30 μm, from greater than or equal to 15 μm to less than orequal to 30 μm, from greater than or equal to 20 μm to less than orequal to 30 μm, or from greater than or equal to 25 μm to less than orequal to 30 μm, and all ranges and sub-ranges between the foregoingvalues. In yet other embodiments, the DOL_(K) of each of the first andsecond compressive layers 120, 122 is from greater than or equal to 5 μmto less than or equal to 25 μm, such as from greater than or equal to 5μm to less than or equal to 20 μm, from greater than or equal to 5 μm toless than or equal to 15 μm, or from greater than or equal to 5 μm toless than or equal to 10 μm, and all ranges and sub-ranges between theforegoing values.

In embodiments, the glass-based article may have a maximum CT greaterthan or equal to 70 MPa, such as greater than or equal to 75 MPa,greater than or equal to 80 MPa, greater than or equal to 85 MPa,greater than or equal to 90 MPa, greater than or equal to 95 MPa,greater than or equal to 100 MPa, greater than or equal to 105 MPa,greater than or equal to 110 MPa, greater than or equal to 110 MPa,greater than or equal to 120 MPa, greater than or equal to 130 MPa,greater than or equal to 140 MPa, greater than or equal to 150 MPa,greater than or equal to 155 MPa, or more. In some embodiments, theglass-based article may have a maximum CT less than or equal to 400 MPa,such as less than or equal to 350 MPa, less than or equal to 300 MPa,less than or equal to 250 MPa, less than or equal to 190 MPa, less thanor equal to 180 MPa, less than or equal to 170 MPa, less than or equalto 160 MPa, less than or equal to 150 MPa, less than or equal to 140MPa, less than or equal to 130 MPa, less than or equal to 120 MPa, lessthan or equal to 110 MPa, or less than or equal to 100 MPa. It should beunderstood that, in embodiments, any of the above ranges may be combinedwith any other range. However, in other embodiments, the glass articlemay have a maximum CT from greater than or equal to 70 MPa to less thanor equal to 400 MPa, such as from greater than or equal to 90 MPa toless than or equal to 350 MPa, from greater than or equal to 110 MPa toless than or equal to 200 MPa, from greater than or equal to 120 MPa toless than or equal to 180 MPa, from greater than or equal to 130 MPa toless than or equal to 160 MPa, or from greater than or equal to 140 MPato less than or equal to 150 MPa, and all ranges and sub-ranges betweenthe foregoing values.

In embodiments, the maximum central tension (CT) may also be describedwith reference to the thickness of the glass-based article. Inembodiments, the glass-based article may have a maximum CT less than orequal to 360/√(t) MPa where t is in mm, such as less than or equal to350/√(t) MPa, less than or equal to 330/√(t) MPa, less than or equal to310/√(t) MPa, less than or equal to 300/√(t) MPa, less than or equal to280/√(t) MPa, less than or equal to 260/√(t) MPa, less than or equal to240/√(t) MPa, less than or equal to 220/√(t) MPa, less than or equal to200/√(t) MPa, less than or equal to 190/√(t) MPa, less than or equal to180/√(t) MPa, less than or equal to 170/√(t) MPa, less than or equal to160/√(t) MPa, less than or equal to 150/√(t) MPa, less than or equal to140/√(t) MPa, less than or equal to 130/√(t) MPa, less than or equal to120/√(t) MPa, less than or equal to 110/√(t) MPa, less than or equal to100/√(t) MPa, less than or equal to 90/√(t) MPa, less than or equal to80/√(t) MPa, less than or equal to 70/√(t) MPa, or less. In embodiments,the glass-based article may have a maximum CT greater than or equal to60/√(t) MPa where t is in mm, such as greater than or equal to 70/√(t)MPa, greater than or equal to 80/√(t) MPa, greater than or equal to90/√(t) MPa, greater than or equal to 100/√(t) MPa, greater than orequal to 110/√(t) MPa, greater than or equal to 120/√(t) MPa, greaterthan or equal to 130/√(t) MPa, greater than or equal to 140/√(t) MPa,greater than or equal to 150/√(t) MPa, greater than or equal to 160/√(t)MPa, greater than or equal to 170/√(t) MPa, greater than or equal to180/√(t) MPa, greater than or equal to 190/√(t) MPa, greater than orequal to 200/√(t) MPa, greater than or equal to 220/√(t) MPa, greaterthan or equal to 240/√(t) MPa, greater than or equal to 260/√(t) MPa,greater than or equal to 280/√(t) MPa, greater than or equal to 300/√(t)MPa, greater than or equal to 320/√(t) MPa, greater than or equal to340/√(t) MPa, greater than or equal to 350/√(t) MPa, or more. Inembodiments, the glass-based article may have a maximum CT from greaterthan or equal to 60/√(t) MPa to less than or equal to 360/√(t) MPa wheret is in mm, such as from greater than or equal to 70/√(t) MPa to lessthan or equal to 350/√(t) MPa, from greater than or equal to 80/√(t) MPato less than or equal to 340/√(t) MPa, from greater than or equal to90/√(t) MPa to less than or equal to 320/√(t) MPa, from greater than orequal to 90/√(t) MPa to less than or equal to 300/√(t) MPa, from greaterthan or equal to 100/√(t) MPa to less than or equal to 280/√(t) MPa,from greater than or equal to 120/√(t) MPa to less than or equal to260/√(t) MPa, from greater than or equal to 140/√(t) MPa to less than orequal to 240/√(t) MPa, from greater than or equal to 160/√(t) MPa toless than or equal to 220/√(t) MPa, from greater than or equal to180/√(t) MPa to less than or equal to 200/√(t) MPa, and all ranges andsub-ranges between the foregoing values.

The glass-based articles may have any appropriate depth of compression(DOC). In embodiments, the DOC is from greater than or equal to 75 μm toless than or equal to 300 μm, such as from greater than or equal to 85μm to less than or equal to 290 μm, from greater than or equal to 95 μmto less than or equal to 280 μm, from greater than or equal to 100 μm toless than or equal to 270 μm, from greater than or equal to 110 μm toless than or equal to 260 μm, from greater than or equal to 120 μm toless than or equal to 250 μm, from greater than or equal to 130 μm toless than or equal to 240 μm, from greater than or equal to 140 μm toless than or equal to 230 μm, from greater than or equal to 150 μm toless than or equal to 220 μm, from greater than or equal to 160 μm toless than or equal to 210 μm, from greater than or equal to 170 μm toless than or equal to 200 μm, from greater than or equal to 180 μm toless than or equal to 190 μm, and all ranges and sub-ranges between theforegoing values.

The DOC is provided in some embodiments herein as a portion of thethickness (t) of the glass-based article. In embodiments, the glassarticles may have a depth of compression (DOC) from greater than orequal to 0.15t to less than or equal to 0.40t, such as from greater thanor equal to 0.18t to less than or equal to 0.38t, or from greater thanor equal to 0.19t to less than or equal to 0.36t, from greater than orequal to 0.20t to less than or equal to 0.34t, from greater than orequal to 0.18t to less than or equal to 0.32t, from greater than orequal to 0.19t to less than or equal to 0.30t, from greater than orequal to 0.20t to less than or equal to 0.29t, from greater than orequal to 0.21t to less than or equal to 0.28t, from greater than orequal to 0.22t to less than or equal to 0.27t, from greater than orequal to 0.23t to less than or equal to 0.26t, or from greater than orequal to 0.24t to less than or equal to 0.25t, and all ranges andsub-ranges between the foregoing values.

In embodiments, the glass-based articles may be characterized by anyappropriate value of DOC/t. For example, DOC/t may be greater than orequal to 0.12, such as greater than or equal to 0.13, greater than orequal to 0.14, greater than or equal to 0.15, greater than or equal to0.16, greater than or equal to 0.17, greater than or equal to 0.18,greater than or equal to 0.19, greater than or equal to 0.20, greaterthan or equal to 0.21, greater than or equal to 0.22, greater than orequal to 0.23, or more.

The glass-based articles may be formed by exposing glass-basedsubstrates to an ion exchange solution to form a glass-based articlehaving a compressive stress layer extending from a surface of theglass-based article to a depth of compression. The ion exchange processmay be conducted under conditions sufficient to produce a glass-basedarticle satisfying any of the frangibility limits described herein. Inembodiments, the ion exchange solution may be molten nitrate salt. Insome embodiments, the ion exchange solution may be molten KNO₃, moltenNaNO₃, or combinations thereof. In certain embodiments, the ion exchangesolution may comprise less than about 95% molten KNO₃, such as less thanabout 90% molten KNO₃, less than about 80% molten KNO₃, less than about70% molten KNO₃, less than about 60% molten KNO₃, or less than about 50%molten KNO₃. In certain embodiments, the ion exchange solution maycomprise at least about 5% molten NaNO₃, such as at least about 10%molten NaNO₃, at least about 20% molten NaNO₃, at least about 30% moltenNaNO₃, or at least about 40% molten NaNO₃. In other embodiments, the ionexchange solution may comprise about 95% molten KNO₃ and about 5% moltenNaNO₃, about 94% molten KNO₃ and about 6% molten NaNO₃, about 93% moltenKNO₃ and about 7% molten NaNO₃, about 80% molten KNO₃ and about 20%molten NaNO₃, about 75% molten KNO₃ and about 25% molten NaNO₃, about70% molten KNO₃ and about 30% molten NaNO₃, about 65% molten KNO₃ andabout 35% molten NaNO₃, or about 60% molten KNO₃ and about 40% moltenNaNO₃, and all ranges and sub-ranges between the foregoing values. Inembodiments, other sodium and potassium salts may be used in the ionexchange solution, such as, for example sodium or potassium nitrites,phosphates, or sulfates. In some embodiments, the ion exchange solutionmay include lithium salts, such as LiNO₃.

The glass-based substrate may be exposed to the ion exchange solution bydipping the glass-based substrate into a bath of the ion exchangesolution, spraying the ion exchange solution onto the glass-basedsubstrate, or otherwise physically applying the ion exchange solution tothe glass-based substrate. Upon exposure to the glass-based substrate,the ion exchange solution may, according to embodiments, be at atemperature from greater than or equal to 340° C. to less than or equalto 500° C., such as from greater than or equal to 350° C. to less thanor equal to 490° C., from greater than or equal to 360° C. to less thanor equal to 480° C., from greater than or equal to 370° C. to less thanor equal to 470° C., from greater than or equal to 380° C. to less thanor equal to 460° C., from greater than or equal to 390° C. to less thanor equal to 450° C., from greater than or equal to 400° C. to less thanor equal to 440° C., from greater than or equal to 410° C. to less thanor equal to 430° C., equal to 420° C., and all ranges and sub-rangesbetween the foregoing values. In embodiments, the glass composition maybe exposed to the ion exchange solution for a duration from greater thanor equal to 2 hours to less than or equal to 48 hours, such as fromgreater than or equal to 4 hours to less than or equal to 44 hours, fromgreater than or equal to 8 hours to less than or equal to 40 hours, fromgreater than or equal to 12 hours to less than or equal to 36 hours,from greater than or equal to 16 hours to less than or equal to 32hours, from greater than or equal to 20 hours to less than or equal to28 hours, equal to 24 hours, and all ranges and sub-ranges between theforegoing values.

The ion exchange process may be performed in an ion exchange solutionunder processing conditions that provide an improved compressive stressprofile as disclosed, for example, in U.S. Patent ApplicationPublication No. 2016/0102011, which is incorporated herein by referencein its entirety. In some embodiments, the ion exchange process may beselected to form a parabolic stress profile in the glass articles, suchas those stress profiles described in U.S. Patent ApplicationPublication No. 2016/0102014, which is incorporated herein by referencein its entirety.

After an ion exchange process is performed, it should be understood thata composition at the surface of the glass-based article is differentthan the composition of the glass-based substrate before it undergoes anion exchange process. This results from one type of alkali metal ion inthe as-formed glass, such as, for example Li⁺ or Na⁺, being replacedwith larger alkali metal ions, such as, for example Na⁺ or K⁺,respectively. However, the glass composition at or near the center ofthe depth of the glass article will, in embodiments, still have thecomposition of the glass-based substrate.

The glass-based substrates that are ion exchanged to form theglass-based articles may have any appropriate composition, such asalkali aluminosilicate compositions. In embodiments, the glass-basedsubstrates include SiO₂, Al₂O₃, B₂O₃, and at least one alkali metaloxide. The at least one alkali metal oxide facilitates the ion exchangeof the glass-based substrates. For example, the glass-based substratemay include Li₂O and/or Na₂O that facilitate the exchange of Na⁺ and K⁺ions into the glass-based substrate to form the glass-based articles. Asdiscussed above, the composition of the glass-based substrates may beequivalent to the composition at the center of the glass-based article.

In embodiments of glass-based substrates described herein, theconcentration of constituent components (e.g., SiO₂, Al₂O₃, Li₂O, andthe like) are given in mole percent (mol %) on an oxide basis, unlessotherwise specified. Components of the glass-based substrate accordingto embodiments are discussed individually below. It should be understoodthat any of the variously recited ranges of one component may beindividually combined with any of the variously recited ranges for anyother component.

In embodiments of the glass-based substrates disclosed herein, SiO₂ isthe largest constituent and, as such, SiO₂ is the primary constituent ofthe glass network formed from the glass composition. Pure SiO₂ has arelatively low CTE and is alkali free. However, pure SiO₂ has a highmelting point. Accordingly, if the concentration of SiO₂ in theglass-based substrate is too high, the formability of the glasscomposition may be diminished as higher concentrations of SiO₂ increasethe difficulty of melting the glass, which, in turn, adversely impactsthe formability of the glass. In embodiments, the glass-based substrategenerally comprises SiO₂ in an amount from greater than or equal to 50.0mol % to less than or equal to 75.0 mol %, and all ranges and sub-rangesbetween the foregoing values. In embodiments, the glass-based substratecomprises SiO₂ in an amount from greater than or equal to 51.0 mol % toless than or equal to 74.0 mol %, such as from greater than or equal to52.0 mol % to less than or equal to 73.0 mol %, from greater than orequal to 53.0 mol % to less than or equal to 72.0 mol %, from greaterthan or equal to 54.0 mol % to less than or equal to 71.0 mol %, fromgreater than or equal to 55.0 mol % to less than or equal to 70.0 mol %,from greater than or equal to 56.0 mol % to less than or equal to 69.0mol %, from greater than or equal to 57.0 mol % to less than or equal to68.0 mol %, from greater than or equal to 58.0 mol % to less than orequal to 67.0 mol %, from greater than or equal to 60.0 mol % to lessthan or equal to 66.0 mol %, from greater than or equal to 61.0 mol % toless than or equal to 65.0 mol %, from greater than or equal to 62.0 mol% to less than or equal to 64.0 mol %, from greater than or equal to63.0 mol % to less than or equal to 64.0 mol %, and all ranges andsub-ranges between the foregoing values.

The glass-based substrate of embodiments may further comprise Al₂O₃.Al₂O₃ may serve as a glass network former, similar to SiO₂. Al₂O₃ mayincrease the viscosity of the glass composition due to its tetrahedralcoordination in a glass melt formed from a glass composition, decreasingthe formability of the glass composition when the amount of Al₂O₃ is toohigh. However, when the concentration of Al₂O₃ is balanced against theconcentration of SiO₂ and the concentration of alkali oxides in theglass-based substrate, Al₂O₃ can reduce the liquidus temperature of theglass melt, thereby enhancing the liquidus viscosity and improving thecompatibility of the glass composition with certain forming processes,such as the fusion forming process. In embodiments, the glass-basedsubstrate generally comprises Al₂O₃ in a concentration of from greaterthan or equal to 4 mol % to less than or equal to 25.0 mol %, and allranges and sub-ranges between the foregoing values. In embodiments, theglass-based substrate comprises Al₂O₃ in an amount from greater than orequal to 5.0 mol % to less than or equal to 24.5 mol %, such as fromgreater than or equal to 6 mol % to less than or equal to 24.0 mol %,from greater than or equal to 7 mol % to less than or equal to 23.5 mol%, from greater than or equal to 8 mol % to less than or equal to 23.0mol %, from greater than or equal to 9 mol % to less than or equal to22.5 mol %, from greater than or equal to 10 mol % to less than or equalto 22.0 mol %, from greater than or equal to 11 mol % to less than orequal to 21.5 mol %, from greater than or equal to 12 mol % to less thanor equal to 21.0 mol %, from greater than or equal to 13 mol % to lessthan or equal to 20.5 mol %, from greater than or equal to 14 mol % toless than or equal to 20.0 mol %, from greater than or equal to 15 mol %to less than or equal to 19.5 mol %, or from greater than or equal to 16mol % to less than or equal to 19.0 mol %, and all ranges and sub-rangesbetween the foregoing values.

Like SiO₂ and Al₂O₃, B₂O₃ may be added to the glass-based substrate as anetwork former, thereby reducing the meltability and formability of theglass composition. Thus, B₂O₃ may be added in amounts that do not overlydecrease these properties. In embodiments, the glass-based substrate maycomprise B₂O₃ in amounts from greater than or equal to 0 mol % B₂O₃ toless than or equal to 8.0 mol % B₂O₃, and all ranges and sub-rangesbetween the foregoing values. In embodiments, the glass-based substratecomprises B₂O₃ in amounts from greater than or equal to 0.5 mol % toless than or equal to 7.5 mol %, such as greater than or equal to 1.0mol % to less than or equal to 7.0 mol %, greater than or equal to 1.5mol % to less than or equal to 6.5 mol %, greater than or equal to 2.0mol % to less than or equal to 6.0 mol %, greater than or equal to 2.5mol % to less than or equal to 5.5 mol %, greater than or equal to 3.0mol % to less than or equal to 5.0 mol %, or greater than or equal to3.5 mol % to less than or equal to 4.5 mol %, and all ranges andsub-ranges between the foregoing values.

The inclusion of Li₂O in the glass-based substrate allows for bettercontrol of an ion exchange process and further reduces the softeningpoint of the glass, thereby increasing the manufacturability of theglass. In embodiments, the glass-based substrate generally comprisesLi₂O in an amount from greater than 8.0 mol % to less than or equal to18.0 mol %, and all ranges and sub-ranges between the foregoing values.In embodiments, the glass-based substrate comprises Li₂O in an amountfrom greater than or equal to 8.5 mol % to less than or equal to 17.5mol %, such as from greater than or equal to 9.0 mol % to less than orequal to 17.0 mol %, from greater than or equal to 9.5 mol % to lessthan or equal to 16.5 mol %, from greater than or equal to 10.0 mol % toless than or equal to 16.0 mol %, from greater than or equal to 10.5 mol% to less than or equal to 15.5 mol %, from greater than or equal to11.0 mol % to less than or equal to 15.0 mol %, from greater than orequal to 11.5 mol % to less than or equal to 14.5 mol %, from greaterthan or equal to 12.0 mol % to less than or equal to 14.0 mol %, or fromgreater than or equal to 12.5 mol % to less than or equal to 13.5 mol %,and all ranges and sub-ranges between the foregoing values. In someembodiments, the glass-based substrate may be substantially free or freeof Li₂O.

According to embodiments, the glass-based substrate may comprise alkalimetal oxides other than or in addition to Li₂O, such as Na₂O. Na₂O aidsin the ion exchangeability of the glass composition, and also improvesthe formability, and thereby manufacturability, of the glasscomposition. However, if too much Na₂O is added to the glass-basedsubstrate, the CTE may be too low, and the melting point may be toohigh. In embodiments, the glass-based substrate generally comprises Na₂Oin an amount from greater than or equal to 0.5 mol % Na₂O to less thanor equal to 20.0 mol % Na₂O, and all ranges and sub-ranges between theforegoing values. In embodiments, the glass-based substrate comprisesNa₂O in an amount from greater than or equal to 1.0 mol % to less thanor equal to 18 mol %, such as from greater than or equal to 1.5 mol % toless than or equal to 16 mol %, from greater than or equal to 2.0 mol %to less than or equal to 14 mol %, from greater than or equal to 2.5 mol% to less than or equal to 12 mol %, from greater than or equal to 3.0mol % to less than or equal to 10 mol %, from greater than or equal to3.5 mol % to less than or equal to 8 mol %, or from greater than orequal to 4.0 mol % to less than or equal to 6 mol %, and all ranges andsub-ranges between the foregoing values. In some embodiments, theglass-based substrate may be substantially free or free of Na₂O.

Like Na₂O, K₂O also promotes ion exchange and increases the DOC of acompressive stress layer. However, adding K₂O may cause the CTE may betoo low, and the melting point may be too high. In some embodiment, theglass-based substrate can include K₂O. In embodiments, the glasscomposition is substantially free of potassium. As used herein, the term“substantially free” means that the component is not added as acomponent of the batch material even though the component may be presentin the final glass in very small amounts as a contaminant, such as lessthan 0.01 mol %. In other embodiments, K₂O may be present in theglass-based substrate in amounts less than 1 mol %.

MgO lowers the viscosity of a glass, which enhances the formability andmanufacturability of the glass. The inclusion of MgO in the glass-basedsubstrate also improves the strain point and the Young's modulus of theglass composition, and may also improve the ion exchange ability of theglass. However, when too much MgO is added to the glass composition, thedensity and the CTE of the glass composition increase undesirably. Inembodiments, the glass-based substrate generally comprises MgO in aconcentration of from greater than or equal to 0 mol % to less than orequal to 17.5 mol %, and all ranges and sub-ranges between the foregoingvalues. In embodiments, the glass-based substrate comprises MgO in anamount from greater than or equal to 0.5 mol % to less than or equal to17.0 mol %, such as from greater than or equal to 1.0 mol % to less thanor equal to 16.5 mol %, from greater than or equal to 1.5 mol % to lessthan or equal to 16.0 mol %, from greater than or equal to 2.0 mol % toless than or equal to 15.5 mol %, from greater than or equal to 2.5 mol% to less than or equal to 15.0 mol %, from greater than or equal to 3.0mol % to less than or equal to 14.5 mol %, from greater than or equal to3.5 mol % to less than or equal to 14.0 mol %, from greater than orequal to 4.0 mol % to less than or equal to 13.5 mol %, from greaterthan or equal to 4.5 mol % to less than or equal to 13.0 mol %, fromgreater than or equal to 5.0 mol % to less than or equal to 12.5 mol %,from greater than or equal to 5.5 mol % to less than or equal to 12.0mol %, from greater than or equal to 6.0 mol % to less than or equal to11.5 mol %, from greater than or equal to 6.5 mol % to less than orequal to 11.0 mol %, from greater than or equal to 7.0 mol % to lessthan or equal to 10.5 mol %, from greater than or equal to 7.5 mol % toless than or equal to 10.0 mol %, from greater than or equal to 8.0 mol% to less than or equal to 9.5 mol %, or from greater than or equal to8.5 mol % to less than or equal to 9.0 mol %, and all ranges andsub-ranges between the foregoing values.

CaO lowers the viscosity of a glass, which enhances the formability, thestrain point and the Young's modulus, and may improve the ion exchangeability. However, when too much CaO is added to the glass-basedsubstrate, the density and the CTE of the glass composition increase. Inembodiments, the glass-based substrate generally comprises CaO in aconcentration of from greater than or equal to 0 mol % to less than orequal to 4.0 mol %, and all ranges and sub-ranges between the foregoingvalues. In embodiments, the glass-based substrate comprises CaO in anamount from greater than or equal to 0.5 mol % to less than or equal to3.5 mol %, such as from greater than or equal to 1.0 mol % to less thanor equal to 3.0 mol %, or from greater than or equal to 1.5 mol % toless than or equal to 2.5 mol %, and all ranges and sub-ranges betweenthe foregoing values.

TiO₂ also contributes to the increased toughness of the glass, whilealso simultaneously softening the glass. However, when too much TiO₂ isadded to the glass composition, the glass becomes susceptible todevitrification and exhibits an undesirable coloration. In embodiments,the glass-based substrate comprises TiO₂, such as in a concentration offrom greater than or equal to 0 mol % to less than or equal to 2.0 mol%, and all ranges and sub-ranges between the foregoing values. Inembodiments, the glass-based substrate comprises TiO₂ in an amount fromgreater than or equal to 0.5 mol % to less than or equal to 1.5 mol %.In some embodiments, the glass-based substrate is free or substantiallyfree of TiO₂.

ZrO₂ contributes to the toughness of the glass. However, when too muchZrO₂ is added to the glass composition, undesirable zirconia inclusionsmay be formed in the glass due at least in part to the low solubility ofZrO₂ in the glass. In embodiments, the glass-based substrate comprisesZrO₂, such as in a concentration of from greater than or equal to 0 mol% to less than or equal to 2.5 mol %, and all ranges and sub-rangesbetween the foregoing values. In embodiments, the glass-based substratecomprises ZrO₂ in an amount from greater than or equal to 0.5 mol % toless than or equal to 2.0 mol %, such as from greater than or equal to1.0 mol % to less than or equal to 1.5 mol %, and all ranges andsub-ranges between the foregoing values. In some embodiments, theglass-based substrate is free or substantially free of ZrO₂.

SrO lowers the liquidus temperature of glass compositions disclosedherein. In embodiments, the glass-based substrate may comprise SrO inamounts from greater than or equal to 0 mol % to less than or equal to2.0 mol %, such as from greater than or equal to 0.2 mol % to less thanor equal to 1.5 mol %, or from greater than or equal to 0.4 mol % toless than or equal to 1.0 mol %, and all ranges and sub-ranges betweenthe foregoing values. In some embodiments, the glass-based substrate maybe substantially free or free of SrO.

In embodiments, the glass-based substrate may optionally include one ormore fining agents. In some embodiments, the fining agents may include,for example, SnO₂. In such embodiments, SnO₂ may be present in theglass-based substrate in an amount less than or equal to 0.2 mol %, suchas from greater than or equal to 0 mol % to less than or equal to 0.1mol %, and all ranges and sub-ranges between the foregoing values. Inother embodiments, SnO₂ may be present in the glass-based substrate inan amount from greater than or equal to 0 mol % to less than or equal to0.2 mol %, or greater than or equal to 0.1 mol % to less than or equalto 0.2 mol %, and all ranges and sub-ranges between the foregoingvalues. In some embodiments, the glass-based substrate may besubstantially free or free of SnO₂.

In embodiments, the glass-based substrate may be substantially free ofone or both of arsenic and antimony. In other embodiments, theglass-based substrate may be free of one or both of arsenic andantimony.

In one or more embodiments, the glass-based articles described hereinmay exhibit an amorphous microstructure and may be substantially free ofcrystals or crystallites. In other words, the glass-based articles mayexclude glass ceramic materials in some embodiments.

The glass-based substrate may include a glass ceramic. The glass ceramicmay include any appropriate crystal structure, such as lithium silicate,beta-spodumene, or spinel crystal structures. The glass ceramiccontaining glass-based substrates may be formed by any appropriatemethod, such as ceramming a precursor glass.

The glass-based substrates may be produced by any appropriate method. Inembodiments, the glass-based substrates may be formed by processincluding slot forming, float forming, rolling processes, and fusionforming processes. Drawing processes for forming glass-based substrates,are desirable because they allow a thin glass article to be formed withfew defects.

The glass-based substrates may be characterized by the manner in whichit may be formed. For instance, the glass-based substrate may becharacterized as float-formable (i.e., formed by a float process),down-drawable and, in particular, fusion-formable or slot-drawable(i.e., formed by a down draw process such as a fusion draw process or aslot draw process).

Some embodiments of the glass-based articles described herein may beformed by a down-draw process. Down-draw processes produce glass-basedsubstrates having a uniform thickness that possess relatively pristinesurfaces. Because the average flexural strength of the glass-basedsubstrate and resulting glass-based article is controlled by the amountand size of surface flaws, a pristine surface that has had minimalcontact has a higher initial strength. In addition, down drawnglass-based substrates have a very flat, smooth surface that can be usedin its final application without costly grinding and polishing.

Some embodiments of the glass-based substrates may be described asfusion-formable (i.e., formable using a fusion draw process). The fusionprocess uses a drawing tank that has a channel for accepting moltenglass raw material. The channel has weirs that are open at the top alongthe length of the channel on both sides of the channel. When the channelfills with molten material, the molten glass overflows the weirs. Due togravity, the molten glass flows down the outside surfaces of the drawingtank as two flowing glass films. These outside surfaces of the drawingtank extend down and inwardly so that they join at an edge below thedrawing tank. The two flowing glass films join at this edge to fuse andform a single flowing glass article. The fusion draw method offers theadvantage that, because the two glass films flowing over the channelfuse together, neither of the outside surfaces of the resultingglass-based substrate comes in contact with any part of the apparatus.Thus, the surface properties of the fusion drawn glass-based substrateare not affected by such contact.

Some embodiments of the glass-based substrates described herein may beformed by a slot draw process. The slot draw process is distinct fromthe fusion draw method. In slot draw processes, the molten raw materialglass is provided to a drawing tank. The bottom of the drawing tank hasan open slot with a nozzle that extends the length of the slot. Themolten glass flows through the slot/nozzle and is drawn downward as acontinuous glass-based substrate and into an annealing region.

The glass-based articles disclosed herein may be incorporated intoanother article such as an article with a display (or display articles)(e.g., consumer electronics, including mobile phones, tablets,computers, navigation systems, and the like), architectural articles,transportation articles (e.g., automobiles, trains, aircraft, sea craft,etc.), appliance articles, or any article that requires sometransparency, scratch-resistance, abrasion resistance or a combinationthereof. An exemplary article incorporating any of the glass-basedarticles disclosed herein is shown in FIGS. 12A and 12B. Specifically,FIGS. 12A and 12B show a consumer electronic device 200 including ahousing 202 having front 204, back 206, and side surfaces 208;electrical components (not shown) that are at least partially inside orentirely within the housing and including at least a controller, amemory, and a display 210 at or adjacent to the front surface of thehousing; and a cover substrate 212 at or over the front surface of thehousing such that it is over the display. The cover substrate 212 and/orthe housing may include any of the glass-based articles disclosedherein.

All ranges disclosed in this specification include any and all rangesand subranges encompassed by the broadly disclosed ranges whether or notexplicitly stated before or after a range is disclosed.

It will be apparent to those skilled in the art that variousmodifications and variations can be made to the embodiments describedherein without departing from the spirit and scope of the claimedsubject matter. Thus, it is intended that the specification cover themodifications and variations of the various embodiments described hereinprovided such modification and variations come within the scope of theappended claims and their equivalents.

What is claimed is:
 1. A glass-based article, comprising: a firstsurface; a second surface; and a stress profile having a firstcompressive region extending from a first surface to a first depth ofcompression DOC₁, a second compressive region extending from a secondsurface to a second depth of compression DOC₂, and a tensile regionextending from DOC₁ to DOC₂, wherein the tensile region has a tensilestress factor K_(T) greater than or equal to 1.31 MPa·√(m) and less than1.8·K_(IC), wherein K_(IC) is the fracture toughness of a glass-basedsubstrate having the same composition as the center of the glass-basedarticle.
 2. The glass-based article of claim 1, wherein K_(T) is greaterthan or equal to 1.41 MPa·√(m).
 3. The glass-based article of claim 1,wherein K_(T) is less than or equal to 1.781·√K_(IC).
 4. The glass-basedarticle of claim 1, wherein K_(IC) is greater than or equal to 1.3MPa·√(m).
 5. The glass-based article of claim 1, wherein DOC₁=DOC₂, asmeasured from the first and second surfaces, respectively.
 6. Theglass-based article of claim 1, wherein the glass-based article isnon-frangible.
 7. A consumer electronic product, comprising: a housingcomprising a front surface, a back surface and side surfaces; electricalcomponents at least partially within the housing, the electricalcomponents comprising at least a controller, a memory, and a display,the display at or adjacent the front surface of the housing; and a coversubstrate disposed over the display, wherein a portion of at least oneof the housing or the cover substrate comprises the glass-based articleof claim
 1. 8. A glass-based article: a surface; and a stress profilehaving a compressive region extending from a surface to a depth ofcompression DOC, and a tensile region, wherein the tensile region has atensile stress factor K_(T) greater than or equal to 1.31 MPa·√(m) andless than or equal to K^(limit) _(T), where K^(limit) _(T) is definedby:$K_{T}^{limit} = {{1.716 \cdot K_{IC}}\sqrt{1 + {2.263\;\frac{DOC}{t}}}}$wherein K_(IC) is the fracture toughness of a glass-based substratehaving the same composition as the center of the glass-based article,and t is the thickness of the glass-based article.
 9. The glass-basedarticle of claim 8, wherein K_(T) is greater than or equal to 1.41MPa·√(m).
 10. The glass-based article of claim 8, wherein$\frac{DOC}{t}$ is greater than 0.12.
 11. The glass-based article ofclaim 8, wherein K_(IC) is greater than or equal to 0.67 MPa·√(m). 12.The glass-based article of claim 8, wherein the glass-based article isnon-frangible.
 13. A consumer electronic product, comprising: a housingcomprising a front surface, a back surface and side surfaces; electricalcomponents at least partially within the housing, the electricalcomponents comprising at least a controller, a memory, and a display,the display at or adjacent the front surface of the housing; and a coversubstrate disposed over the display, wherein a portion of at least oneof the housing or the cover substrate comprises the glass-based articleof claim
 8. 14. A glass-based article, comprising: a first surface; asecond surface; and a stress profile having a first compressive regionextending from a first surface to a first depth of compression DOC₁, asecond compressive region extending from a second surface to a seconddepth of compression DOC₂, and a tensile region extending from DOC₁ toDOC₂, wherein the tensile region has a tensile stress factor KT greaterthan or equal to 1.31 MPa·√(m) and less than or equal to K^(limit) _(T),where K^(limit) _(t) is defined by:$K_{T}^{limit} = {{2.504 \cdot K_{IC}}\sqrt{1 - {0.531\frac{{{DOC}_{1} - {DOC}_{2}}}{t}}}}$wherein K_(IC) is the fracture toughness of a glass-based substratehaving the same composition as the center of the glass-based article, tis the thickness of the glass-based article, and the DOC₁ and the DOC₂are measured from the first surface.
 15. The glass-based article ofclaim 14, wherein K_(T) is greater than or equal to 1.41 MPa·√(m). 16.The glass-based article of claim 14, wherein K_(T) is less than or equalto 0.95·K^(limit) _(T).
 17. The glass-based article of claim 14, whereinK_(IC) is greater than or equal to 0.67 MPa·√(m).
 18. The glass-basedarticle of claim 14, wherein DOC₁=t-DOC₂.
 19. The glass-based article ofclaim 14, wherein the glass-based article is non-frangible.
 20. Aconsumer electronic product, comprising: a housing comprising a frontsurface, a back surface and side surfaces; electrical components atleast partially within the housing, the electrical components comprisingat least a controller, a memory, and a display, the display at oradjacent the front surface of the housing; and a cover substratedisposed over the display, wherein a portion of at least one of thehousing or the cover substrate comprises the glass-based article ofclaim
 14. 21. A glass-based article, comprising: a surface; and a stressprofile having a compressive region extending from a surface to a depthof compression DOC, and a tensile region, wherein the compressive regionhas a compressive-stress factor K_(CS), the tensile region has a tensilestress factor K_(T) greater than or equal to 1.31 MPa·√(m), and:${\frac{K_{T}^{2}}{K_{I\; C}^{2}} + {\frac{1}{28.5}\frac{K_{C\; S}^{2}}{K_{I\; C}^{2}}}} \leq 4.45$wherein K_(IC) is the fracture toughness of a glass-based substratehaving the same composition as the center of the glass-based article.22. The glass-based article of claim 21, wherein:${\frac{K_{T}^{2}}{K_{I\; C}^{2}} + {\frac{1}{28.5}\frac{K_{C}^{2}}{K_{I\; C}^{2}}}} \leq {4.1.}$23. The glass-based article of claim 21, wherein K_(T) is greater thanor equal to 1.41 MPa·√(m).
 24. The glass-based article of claim 21,wherein the glass-based article is non-frangible.
 25. A consumerelectronic product, comprising: a housing comprising a front surface, aback surface and side surfaces; electrical components at least partiallywithin the housing, the electrical components comprising at least acontroller, a memory, and a display, the display at or adjacent thefront surface of the housing; and a cover substrate disposed over thedisplay, wherein a portion of at least one of the housing or the coversubstrate comprises the glass-based article of claim 21.